Is it possible to disassemble and repair (or replace) blades on a Swiss Army knife?

It is possible in fact there is a growing aftermarket for customised or “modded” Swiss Army Knives which have been rebuilt to specific configurations. You can specify a particular layout of tools, you can have the aluminium liners replaced with brass and you can have exotic materials ranging from copper, brass, wood and micarta to titanium for the scales.
You can dismantle a Swiss Army Knife with a Dremmel and a very steady hand but other tools such as clamps and vices would be advised – there are many YouTube videos which explain how to do this but reassembling is a little more tricky as you will need to get hold of appropriately sized metal rods or “pin stock” which can be cut and shaped into new pins, I believe that many modders use 2.5mm for the outer pins and 2.2mm for the inner ones. Alternatively some people use bolts but they tend to be I conjunction with exotic scales, if you plan on using the original plastic scales you are better off using pins.
If you simply have a damaged knife then Victorinox offer very generous warranty terms, often you pay no more than postage to a service centre although bear in mind that if the knife is not a current model it may not be repairable and they could send you the modern equivalent as a replacement so if the knife has sentimental value probably best not to do this. If you don’t feel that you have the expertise to dismantle and reassemble the knife yourself and if you think that it is worth the cost, you could send it to one of the many modders around the world who would be able to do the work for you but obviously at a price higher than just replacing the knife with a new one. Likewise if you want a unique knife made to your individual specifications that you could hand on to your descendants then again it may be worth the cost.
I would suggest looking up one of the online forums such as Multitool.org – Reviews on the best Multi tools, Swiss Army Knives, outdoor gear and more. as a good source of additional information and advice.

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