To cut through vinyl with a Jigsaw is to use a very lovely, metal-cutting blade for these applications. Ones that are made from a durable alloy such as bi-metal or high carbon steel are expensive than the more blades on the market but would be ideal for the job. When cutting on plastic with this power tool, there are a few things to keep in mind.
To avert chips on the surface, you should try cutting through the base of the workpiece instead of through the top. The second step would be to use painters tape and stick it on the area that you intend to cut.