I routinely take out of paper mounts, old slides I want to scan. If they need to be in mounts afterward, I put them in Pakon plastic mounts, which are cheap and easy to use. The Pakon plastic mounts are more durable than the plastic mounts and are less likely to jam in projectors.
In general, you just start at a corner and with your fingernail, peel the paper apart. The slide is not "glued" to anything, but rests in a depression in the mount. You will not harm the slide-film by peeling away the paper mount.