Answer:
If you want to filter out the grains then certainly you could using normal filter papers in a filter funnel and repeat until the solution is clear of bits. You could also use a sintered glass filter. However, there will still be compounds from the coffee dissolved in the water and so a molecular sieve could be used and/or a chromatography column to separate these from the water. (You could try reverse osmosis if you really want to try an extreme method and have heaps of lab equipment and time). In practice it is probably easier just to distill the water off in the usual chemical lab way. Of course you could drink the coffee and inevitably separate out the water!
