I'm far from an expert, and there's many people on here with more experience and knowledge than I. That being said, here's what I do.

I wouldn't recommend feeding your snake in it's vivarium. The reason for this is that snakes can begin to associate the cage being opened with food being made available and can respond aggressively.

Get a sweater box, or another container of some sort. Use this as your feeding box. Put the mouse in first, before the snake. I'd recommend putting the mouse in some sort of box as well inside your feeding box. Young snakes in the wild often prey primarily on young rodents in burrows and having the mouse in another container can bring out this response. I'd recommend using a small cardboard box and cut a hole on the side big enough for your snake to fit through.

You can also try stunning the mouse, simply by taking it by the tail and whacking it against a hard surface. I know it may sound cruel, but I've had to do it many times with mine. I've tried without success to feed my snakes f/t mice, and I often did this just to ensure that the mouse couldn't harm the snake. Now I have enough confidence in them to feed them live all the time. You can try dangling the stunned mouse in front of your snake and they'll usually figure it out themselves. Be sure to use long tongs when doing this, so your snake doesn't accidently tag your hand while attempting to strike the mouse!!

What kind of snake do you have, btw?