In most cases cork floor should be sealed in which case using a neutral chemical and washing should be fine however if the cork is not sealed it becomes more challenging. Cork should not be exposed to large amounts of water. Rather if it is not sealed you should use a dry method such as a foam rubber sponge which is like a large eraser without the pumice which are in pink erasers.
The dry sponge or foam rubber sponges are available at any janitorial supply store or hardware or paint stores. Common sponges should not be used. Since cork is so porous be sure absorb as much as possible with a good absorbent towel almost treat it like you would removing a carpet stain, by blotting and absorbing rather than scrubbing. Using stronger chemicals like bleach etc. will damage the cork