If you had to defend yourself with a knife against a violent dog either charging or in the process of attacking one of your own animals

I would drop the knife and use something else.
I have had to defend myself from attacking dogs on several occasions. Before job related injuries prevented it, I ran in order to stay in shape. Many dog owners don’t confine their dogs. And many unrestrained dogs chase runners. Similarly, I rode my bicycle as my sole form of transportation for over five years. Dogs like to chase cyclists almost as much as they like to chase runners. I also lived in rural fly-over country and had dog issues there. Based on my experience, knives don’t benefit much in a dog fight. If fact, they might be a hindrance. If I had a hand-held knife, I wouldn’t use it against a dog.
Of the various times dogs charged me, two come to mind in particular.

I used to raise pygmy goats. One oh-dark thirty, mid-winter Michigan morning, I woke to the sound of goats bleating in distress. I crawled out of bed, pulled my jeans on, walked to the door where my boots were kept, while trying to shake off the grogginess of sleep and listen for sounds other than goats to figure out what was going on. I pulled my boots on sans socks and walked toward the barn looking for signs of prowlers or tweakers looking for scrap metal.
The front barn door was closed. The only other door was the small goat door on the side of the barn. It was closed too. With both doors closed, I jogged back to the front door and opened it to find a German Shepard and a rottweiler attacking a goat while the other goats had retreated to a raised platform built for them. The goat under attack had given up by the time I reached it. It was down on its knees not making a sound. Its eyes were unblinking. The other goats were making plenty of noise.
Neither dog initially paid me much attention. They were focused on their intended kill. The rottweiler had a collar and part of a lead line hanging from the collar. I reached for the shovel I kept next to the goat pen and hit the rottweiler on the back of its head. It dropped. The German-Shepard turned from the goat, faced me, and charged. As it lunged to bite, I shoved the shovel handle into its mouth pushing the handle to the back of the dog’s jaw horizontally, then grabbed it by the throat and pinned it to the wall at my eye-level. I bounced his head off the wall a few times till it stopped trying to bite.
The rottweiler got up and came at me. I dropped the German Shepard and faced the rottweiler. As the rottweiler reached its head in to bite, I side stepped and came down on its neck, pinning its head to the ground. It struggled to free itself. I controlled it by wrapping my legs around the hind part of the rottweiler. Then keeping its head in place with my guard arm pressed across the dog’s throat, I twisted the collar tighter. When the dog submitted, I used what was left of the lead to tie it up.
The German Shepard was gone. It left through the hole the dogs dug to get into the barn.
With one dog gone and the other secured, I went inside, called the police and an emergency veterinary service, then I filled gallon water jugs with hot water, got a blanket, went back to the barn, and wrapped the goat up. I stayed with the goat till the cops showed up three hours later.
The goat lived after the vet cleaned and stitched up over 75 puncture wounds.
The police found the other dog at its owner’s place after tracking it through the nearby field. The dogs were used to guard a meth lab until then. Both dogs got put down.

The second incident involved a Portuguese water dog / mastiff crossbreed. It was a mutt, a big mutt. My brother-in-law brought his dog, the aforementioned crossbreed, to my house while he was trying to get clean and sober, and put his dog in the garage. Previous interaction with the dog went smoothly. So, the dog was given a bed and food in the garage. After that though, he took possession of the garage.
Unfortunately, that was where the laundry was done. My 19 year old daughter went to do her laundry. The dog attacked. My daughter was pinned against the dryer.
I heard my daughter’s screams.
I went to the garage and came in behind the dog who was facing my daughter. I shouted. No impact. I boxed the dog on the side head it turned and came at me. Using my left hand, I slapped the dog across the head. Distraction. As it tried to bite my left hand I grabbed the dog by the throat with my right and pinned it against the refrigerator lifting so it was unable to touch the floor. The dog didn’t like it, and unlike the rottweiler in the previous incident, it had not been softened with a blow to the head with a shovel. It did not submit. So, I brought it down hard on the concrete, pinned its head, then scissored it from behind, then pushed my guard arm, across the dog’s throat just below the jaw making sure to press down and against the lower jaw with my left forearm. With my free right I used a hammer fist on its ears, nose, and eyes. The dog still didn’t submit and was trying to turn to bite. I tried to stretch the dog to limit its struggle. It still didn’t quit. So, I used my right ankle to crush his unneutered groin into sterility. Eventually the dog quit fighting and submitted. I let him up and he limped out the back door. My daughter took her laundry and left.
When my brother-in-law came home I told him the dog was no longer welcome. They left.

Dogs only have one business end, their mouth.
Dogs are faster than you. Never run.
If dogs bite high, they expose their throat. Crush the neck or throat just below the jaw and take them to the ground or wall. Get on top if possible to keep them from using their legs to pull free.
If dog bites low, come down hard around the neck at the base of the skull or just below the jaw. Push sideways a bit to off balance the dog and take it off its feet. Like before, don’t let them use their legs to pull free.
If a dog attacks, don’t try to grab the skin like some people do with kittens or puppies. Many dogs have loose skin or folds of skin. This allows them to turn and bite your hand if you grab skin. Push hard against bone and muscle.
Don’t engage their sides or back or tail till you’ve dealt with the head.
Knives don’t work well. They are too close-up and not flexible enough to immobilize the dog. While they will enable you to beat (kill or seriously injure) the dog eventually, my take is your own risk of injury goes up with a knife. If you swing and miss, the dog will more than likely get your arm or hand. This can cause you to lose the knife or lose the ability to use it.
If you are going to use a weapon other than a firearm, use items that keep distance or give the dog something to bite on other than you. That is much better.
Pepper spray or bear repellent is good. Probably the best. I don’t carry generally. It hasn’t always been a legal option. That leaves me with improvised weapons or my hands and legs.
I’ve used several improvised weapons other than the shovel. I used my bike several times and large sticks, or breaker-bars that I normally used for breaking concrete. I’ve never been tempted to use a knife.

Edit: I’ve trained to deal with knives presented by attackers but do not consider myself well trained in knife fighting. Like most things, I’m sure there are people who’ve put the time and effort into wielding a knife with skill enough to deal with a dog. I don’t put myself in that category. A dog seems trickier with regard to a knife than a person in many respects.
Also, as much as the events might seem grandiose, they are a bit sanitized and simplified e.g. the rottweiler did not drop with one hit; I hit him several times on the head and body and legs before either dog actually turned from attacking the goat. The answer was not intended to be a write-up for a Quentin Tarantino movie with gratuitous violence. Rather, it was intended to address how to defend against a dog attack without a knife when avoiding the fight was not an option from my perspective. It was very up-close and personal. After some thought it seemed like too much of a simplification. I remember thinking, This d**n dog isn’t flinching. How many times do I have to hit this f*****g dog before the goat dies?

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