An animal shot through the vitals shouldn't go far. A gut shot animal would be another story.

I would probably just go in there and quickly drag it back to my property.

This is not a problem I have ever had since my neighbors would never tell me I can't retrieve a deer and I in turn would not do that to them.

Luckely in MN it would also be perfectly legal for me to go in and get the animal without even asking unless they came out and told me to leave in which case I would have tp abide by their wishes.