Use self adhesive wet and dry paper on a flat face plate i.e. no holes! or disc sander. You will need to work up from 120 grit through to the finest paper you can get 1,200 grit as your diamond tile saw will have grit around the 100 mark. Final polish with metal polish on soft plain paper - the type of liquid polish used for silver or jewelers rouge if you are doing a lot of polishing. If you can tolerate a bit of rounding at the circumference then use soft leather as it hold the abrasive (rouge) better than paper. Keep the pressure and speeds low as the friction can melt the acrylic and spoil the finish. I use carborundum grit obtainable from a lapidary supply store in various grits from 40 to 1,200 on leather disks keeping each disk in a separate plastic bag to avoid contamination of the finer grades with grit from the early coarse grit discs. Keep everything clean to avoid the odd bit of big grit ruining the final finish. I use water with a dash of dish washing soap to keep the acrylic cool and help the lose grit to embed in the leather. Olive oil is also used but is a bit messy on the clean up between grit.
Hope this helps. - Regards - Pat