Hi,
What I did was to get a replacement mosfet first. Once you have the replacement on hand I cut the legs off the old mosfet with a scalpel or razor blade. Then I used the soldering iron and a solder sucker to remove the remains of the old mosfet legs. Don't use too much heat with the soldering iron or you might pull up a trace. Gentle and slow are the keywords. Once you see the solder melting (add some fresh solder if you don't see them melting) gently push the leg side ways. Don't pull it up. After that I used soldering braid and solder to clean up the pads though this may not be necessary if the legs come away cleanly.
To install the new mosfet I used some soldering past and dipped some on the legs of the new one. I can't remember if I used a heat gun to solder them on or a soldering iron. It depends on how much room you have. A heat gun would probably be OK but remember to mask off adjacent components. Good luck with the repair.