is your mouse using USB or PS2 port?
if u need to take out the mouse, just use your hand and pull it
out. it shoun't be the probelm.
however, when u plug in back to another computer, please do take
note that if u cannot plugin the USB head, please do not force it.
turn over the head and try plugging in again.
as for PS2 mouse, there is a rectangular male pin which u need to
take note of

please put in gentally until the rectangular male pin slots into
the rectangular female hole