If you do a search on this forum you'll find lengthy discussions.
1) Freeze alive. Not recommended for hoppers and adults ok for pinkies and fuzzies. possibly inhumane depending on who you ask. good for lots of mice.
2) Cervical dislocation. Place an object firmly at base of skull, elevate rear of mouse by tail. Give a sharp jerk on the tail to break neck. can take practice to do correctly. the first time I tried this the mouse spasmed, flopped onto the floor then twitched a few times and died.
3) Hit it in the head very hard with something. can be messy.
4) Put it in a bag or sock. Swing it around fast then hit a table or wall. this was easiest for me since I don't need a lot mice.
5) CO2. Buy dry ice or a paintball CO2 tank. rig it up so the CO2 fills a container from the bottom and pushes air out the top. good for killing lots of mice. more construction details can be found searching the site.
6) if you're squeamish, you may be able to find an electric mousetrap online.
Since you have one snake, everything but the CO2 would be easiest.