I rent out a apartment in Jerusalem with a few other people. We have been affected by mice which come in on a daily basis. We get these traps which are basically pads of glue and they get trapped on the glue and can’t move. They try to escape resulting in them losing there limbs and are in severe pain and agony. Would it be permissible to elevate there suffering by killing them instantly? (Running them over with a car or with a boulder) The alternative is for them to die slowly because of the amount of pain or hunger.
Yes you should kill it in as fast of a way that you can, to alleviate its pain and suffering. In fact there are poskim who discourage using such traps because they cause tzar baalei chayim.
Kovetz Halachos Lmionos Hakayitz ( Harfenes) 1-17, also heard in the name of R’ Scheinberg zt”l