Is it possible to cut the sink out a molded vanity top? We would like to put in a table top style sink, but to do so we need a counter top with a hole for the sink. Trying to save money and use the counter top we already have.
Almost always, yes, (assuming the hole left will be covered by the new sink) but what tooling you need depends what the sink/counter is made from - Something like Corian® (generically, solid surface countertop material) is a lot easier to cut (being just thick plastic) than a stone-like or porcelain-like material - those can be cut but will require diamond tooling and water cooling, usually.
You might be better off looking for a new (or new-to-you - visit your Habitat ReStore, if there's one in range, or similar building materials recycler if that's not applicable to your area) countertop and selling your old top and sink to someone else.