My cat is a real mouser, he catches em all the time.
most of em, he just leaves out back in the "boneyard" (garden).

Sometimes, i wake up, and i see some mouse guts and a head on my tile floor.
The worst is when he brings em in a live.
Then it's up to me, to catch the mouse from the cat to avoid having to clean up mouse guts of my tile floor.
To do that i have to growl louder at the cat, then he growls at me (for attempting to take the mouse).
half the time, the mouse is still in one piece, and still has legs to carry him.
Like these lucky sob's:
the other half, the mouse has a broken back, or serious puncture wounds.
So you got the poor thing on your hand, frightened , in pain, looking at ya. What do you do?
Well, i don't like killing animals, but i hate the idea of prolonged agony more.
The easiest thing, is to flush em down the toilet.. they'll drown in no time.
The most merciful thing, i tried it, is a wooden 2x4, smack it on the mouse.
WARNING: Don't do that inside the house!!
A mouse is basically a little bag of bloodNgutsNpoo.
They are very mercifully dead with a 2x4, instant, no suffering
But after that, you get to clean up the bloodNgutsNpoo that did a major SPLAT! into all directions.
So i'm sticking to the flush method, though i feel slightly sad about the inglorious demise of a little mouse.. They are actually quite cute if you get them close up. I think Squirrels are not much different, just slightly bigger.. Get a 4x4 instead of a 2x4.. post results of the SPLAT!