...okay.
Has it been glued to the desk? If so, what kind of a surface are we talking about? If it's solid wood that's been varnished or painted, you will destroy the coat if you use any kind of solvent that reacts with it. If the desk is made of laminated fiberboard, chances are that you won't damage the colour of the laminate per-se, but moisture might break through it and make it
"bubble up". If you use a solvent that's oil-based, like mineral spirit, it might stain the surface in both cases
(not to mention that the vapour is highly volatile and might explode if the area is not well-ventilated).
You will need a solvent that is just right for the surface you're working with and
a lot of patience so that it penetrates under the paperweight and dissolves the glue. You can occasionally try to speed up the process by insering wedges into the gap between the rock and the wood. You can also use a flat-headed screwdriver, however that might leave unsightly marks on the wood.
If you
really don't care about how the desk will look like after you're done, there's always the option of hammering it off with a hefty hammer and, if needs be, a chisel. If the rock is
really sizable, a trusty crowbar is also an option. The absolute worst bruteforce scenario involves a sledge - the paperweight will come right off... possibly with a part of the desk still stuck to it.
I hope that was inspirational.