Glue Traps do kill mice but the glue rap doesn't kill mice instantly like a snap mouse trap does.
With A Glue Trap the mouse gets stuck to the glue trap and eventually since they cannot get off the glue trap they die which can take a few days to a week.
But once the mouse gets onto the glue trap the mouse will not be able to get off so glue traps are effective to get rid of mice when the other snap traps are not working or they're avoiding the mouse traps.
You can place a bit of food onto the glue trap which will lure the mouse to the glue trap and they'll walk onto the glue trap and become stuck.