If you have a drill you could try a hole cutting attachment, like they use for drilling large holes through doors. It cuts the hole, but also creates a cut-out that must be pried out of the attachment. This can be used for a base. 60mm is about 2 3/8", so if you can find a 2 1/2" hole cutter the resulting cut out should be very close to 60mm. There would be a small drill hole through the base however, but that is easily dealt with. Use tempered hardboard for your base material. Although if you can get some old casing, plastic casing, like from an old tv or vcr or something, that material makes for excellent bases, among other things.
The other alternative is a circle cutter for either a dremel tool or a roto-zip. They are not too expensive (The circle cutters anyway) and are very handy. In any case use something like a rasp or block plane or small modelling plane to bevel the edges to whatever angle you want. I found that I could knock out a good number of 40mm bases for my terminators in very short order.