How to cleanly remove a section of countertop
Usually tops like that are built by fitting a base sheet (usually particle board for flatness and smoothness) and edging it with hardwood using miter joints. Then laminate is applied across the entire surface with contact cement. The laminate is then trimmed flush with a router, and a bevel or more detailed edge is routed into the hardwood and laminate simultaneously. 

Stain (optional) and several coats of high-quality sealer finish the job. With this technique, virtually any shape is achievable with basic carpentry skills.