Cutting magnets can be done, but most materials need to be kept cool. High temperatures will destroy the magnetism of ferrous metals, although I'm not sure about the modern rare-earth magnets.
I wouldn't recommend using a magnet to hold the bridge up, simply because it doesn't have any way to lock it in place. A good bump, such as an errant elbow, could knock the bridge loose, and the trains hit the floor.
I'd use an old-fashioned slide-bolt latch, the kind used on garden gates, mounted on the underside of the bridge. Drill a hole in the layout face, or attach a board under the benchwork if needed, line it with a piece of brass tubing if you want to make sure it will never wear, and align the bolt with the hole. On my gate-style bridge I did all of this BEFORE laying any track, to make sure everything fit tightly, and there was no play when it was locked.
Then, after everything was secure, I laid the roadbed (wood) right across the gaps, at both ends, and the track on that, with extra-wide PC ties on both sides of both gaps for security. Cut the rails and roadbed with a razor saw, and the track lines up perfectly, with no sliding joiners or other fancy stuff. To complicate mine the entire bridge is in the middle of an 18 inch radius curve, and both ends are at odd angles to the track, so this was about the ONLY way to lay it! I've caught my shirt, or arm, on the rail ends several times, with no damage to the track. My arm didn't always come out so well.
In my case, the bolt goes through the face of the fixed layout, and pushes on the actuating plate of an ancient telephone company relay, giving me at least a half-dozen DPDT contacts for signaling and power control. Unless the bolt is all the way in, the track on the bridge, and a short distance on either side, is dead.
