Is it permissible to kill mice using glue traps, which cause them a slow and torturous death, and does this contradict the principle of ihsan (excellence) in killing, which the Messenger of Allah, may Allah's prayers and peace be upon him, called for?

It is not permissible to kill mice by starvation, paralysis, or slow-acting poisons that cause torture, because this violates the command of the Lawgiver to be merciful in killing. The Prophet (peace and blessings be upon him) said: "Indeed, Allah has prescribed excellence in everything. So, when you kill, kill well, and when you slaughter, slaughter well. Let one of you sharpen his blade and relieve his animal."

However, there is no harm in using a trap to catch them and then killing them quickly.