Sure...paper cutters or punches are available in dozens of shapes and sizes. I have 3/4", 1", 1.25", 1.5", 1.75" and 2" round cutters in the shop and use them all the time. Lots of places carry them, including Michaels, Hobby Lobby, Amazon.com, several sellers on Etsy, Zibbet and other places. See the link below for Etsy search results.
For the artwork prep, I normally use a PC application called "Microsoft Visio 2010", then print the art on HP photo paper, cut the rounds out, and then mount the art inside an appropriately sized counterbore in the turning using "Gem-Tac" glue. After the glue is dry, I'll use either a two-part epoxy resin to cover it or a less messy epoxy dome.