One of the great "practical experiments" we used to do, way back in the last century, was to cut the big magnets our of PC hard drives. They make fun toys, and since they were paired, you got two for the price of one. One of the first lessons learned playing with strong magnets is to not let the magnets smack together with any part of your body in between them.
Two kinds of natural forces do not care what parts of your anatomy are caught between them: strong magnets & door jambs. Pliers also rank up there pretty high as well.
At the very least, someone with a sufficiently strong implanted magnet would experience is the pain of magnetic things snapping onto their skin. A little sting here, a small bruise there. Hovering a strong magnet over the implanted magnet will almost certainly cause the character to lose control of the external magnet and will snap smartly onto his skin. Pain & hematoma are certainly possible outcomes. It's also possible to lacerate the skin or puncture it if the edge of the external magnet is at all angled and hits the skin the right way.
As you can see, there is not a lot of tissue above this pacemaker battery pack. If it were a magnet and a strong magnet were brought close enough, they would snap together.
Very few implants are placed under muscle (certain breast implants and almost all orthopedic implants are common exceptions). They're designed not to interfere with the nerves & muscles above. Most implants are nestled cosily in the subcutaneous fat. If you did implant a magnet under the muscle, your character would risk damage to the muscle as well as skin & subcutaneous tissues when the magnets smash together like two miniature planets.
Nerve damage is a possibility if the implanted magnet is under a nerve and the external magnet presses on it for an extended period of time (like a couple hours or more). Unless you are proposing some kind of crazy dystopy, no good surgeon will place an implant under a muscle or major nerve, e.g. in the arm or hand. Implants are frequently placed in the arm (non-magnetic / titanium orthopedic plates & screws; A-V fistula grafts, some hormone therapy delivery mechanisms) but none are intended to interact with external forces, including MRI machines or HDD magnets.
Very strong magnets can indeed cause devastating crush injuries. Strong enough magnets could fairly easily break bone as well as crush soft tissues.
Implant removal is a fairly trivial procedure and is done frequently (removal of orthopedic hardware, removal of breast implants, exchange of pacemaker battery packs). If the implant is done right, and not as the brainchild of some mad scientist, then getting it our should post no difficulty for recovery.
I don't think it would make any difference if the magnets were electromagnets, except that obviously your character would have to activate the internal magnet to be affected by the external magnet.
Phile Under Phun!
Small magnets such as your mad scientician might implant in a character aren't very powerful ... but if your character has a magnetic implant of some kind and comes into the range of a real magnet, then the fun times really begin!
Here's how strong an MRI magnet is, for example. Probably not strong enough to suck your character in, unless the implants are large, but it is possible that it might get torn out of his body or cause pain and discomfort while it's trying to escape the confines of the skin!