Are you allowed to remove a mouse trap with a mouse on it on shabbos?
If it's just the mouse trap (without the mouse in it), it should be a regular kli shemelachto l'issur and can be removed if it's in your path.
With the mouse in it, the trap would be a bassis for the mouse and forbidden to move with your hands, though one may move muktza with any other part of the body. The one loophole (which would defeat the purpose) would be if the mouse was not on the trap sunset Friday, one can release the mouse from the trap with one's foot. The trap, being only a temporary bassis can now be moved if the space is required. Now of course if it is where everyone can see it and it disgusts people then We find a gemora (Shabbos 121b)Rav Ashi told his servant to lift a dead mouse by its tail and remove it from the house. This was to teach that anything sickening or unpleasant in one’s surroundings may be handled directly and removed, despite it being muktze.
Chazal allowed the handling of muktze items in order to save one from unpleasantness.
Rav Moshe Feinstein Ztz”l In the back of the sefer written by Rav Pinchas Bodner called “Muktze quotes the case of guests arriving and there is a muktze itemin the living room that is disturbing, it may be removed in a normal way.
The Mishna Berura in (Simon 308:115) similarly writes that a pile of shells can be removed from the table with one’s hands, even though they are muktze, because one is disgusted by it.
Rav Shlomo Zalman Auerbach Ztz”l 1 says that if guests are arriving and the housewife is greatly embarrassed lest the guests would see even a small amount of shells and peels, then they too may be removed.
Partialy summarized from: