Arborite is an inexpensive and highly durable solution for countertops. Arborite is the stuff most of the countertops of the 1970's were made of, and many of those counters still exist in solid shape today, despite the fact that the older patterns are outdated. It's tough stuff, but in its inlaid form is terribly brittle and susceptible to chipping during cutting.
Use a jigsaw or circular saw with a fine tooth blade. The smaller the tooth, the less likely you are to snag the brittle Arborite, rendering your cut useless. Where possible I recommend the jigsaw. Jigsaws give you the freedom of cutting your Arborite to fit things such as your sink hole perfectly. If you are cutting straight lines, however, a circular saw, or table saw will often do the job best. In either case, the saw blade choice is crucial to a clean cut without chipping.
Use masking tape to true your straight lines for cutting. It will give the remaining Arborite a reason to separate from the masked area and it will give you an easy to follow line for your cuts. It's best to mask the printed side, as that is the piece most important to make chip free. Take the time to mask. Your new counter surface will thank you for your careful diligence through many years to come.
Let the saw do the work. Our tendency when working with power equipment is to push hard, so that we get the most cut per second with our saw. With Arborite, however, that can be a costly mistake. Take your time. Cut slowly and be patient about the cut. The most important rule of thumb in working with power tools to complete a home renovation is this: If you rush the job, it will look like a rush job.
Use plywood when making all of your cuts, no matter how small. The most important piece in the equation when cutting Arborite neatly, without chipping, is to lay it flat against a piece of plywood while cutting through the Arborite and the plywood. If you are cutting a hole, such as for a sink, drill a hole in the portion that will be unused and then use your jigsaw to get to the edges of the hole for the trip around the hole. Place your plywood edge wherever you will start the cut, and make sure to always have plywood as part of your cut. The moment you try to cut a section of any size without a plywood backing, you run the risk of ruining your entire piece of Arborite.