Depends on the type of slime.
If it is the type made with Elmer's glue and Borax (also called Flubber), vinegar works to remove it. Soak it for a few minutes to an hour, then wipe off.
If it is biological (pond algae, egg, aloe vera gel, etc.), try soaking with water to re-hydrate the slime and make it easier to remove. A damp paper towel will hold enough water or vinegar in place to soften the slime without making a big mess.
If water or vinegar doesn't work, you can try solvents such as alcohol (isopropyl rubbing alcohol or hand sanitizer) or mineral spirits. These solvents are more likely to damage the finish of the wood, so I would try plain water first.
There are some materials, like epoxy, that might look like dried slime but are not going to dissolve again. In this case, you might need to chip or sand off the dried material, then refinish the desk with oil or stain and clear coat.
Can you tell me more about the type of slime?
If I know what it is made of, I might be able to give you a more specific suggestion.