Without making a big sloppy mess, give the slate a sponge bath, with some hot, very mildly soapy water, and then rinse with water only, or, you can also use alcohol and water. You might even use a scotchbright pad or steel wool for the scrub down.
Make sure its rinsed well and then let it dry for a few days before you re cloth. You can also use a fan or space heater to encourage drying.
Beer, soda, and other unknown liquids can leave the slate "sticky" which can cause all kinds of funky issues under the cloth. The cloth itself can get stuck to the slate, chalk dust will stick and build up( rather than being vacuumed away) , humidity will dampen the sticky spot which can in turn dampen the cloth, if its real bad the stickyness can even wick up to the surface of the cloth which is like a nightmare on elm street.
* cue scary music*
You might not remove the stain itself but at least clean up any possible residue on the surface.