The concept of playing Skyrim as a vegan is very immersion-breaking, but it also makes for quite a challenge. You cannot use anything that has animal components in it, so that means a lot of potions, armor, armor upgrades, arrows, and food products cannot be used or consumed. Animals cannot be killed except for plot reasons, you cannot ride horses, no use of dragon souls (and thus a lot of shouts cannot be used) and several spells are restricted.
Sound fun yet? There is certainly no restriction on killing humanoids, so go clean up that bandit hideout full of leather and hide-wearing heathens.