Does cutting a straight groove require multiaxis programming?

It sure does if you are cutting it using an industrial robot. Traditionally these machines have been used for loading/unloading, painting, gluing, or welding applications, but thanks to the advances in guidance control they are getting more precise and adaptable. Many companies now use them for deburring, prototyping, and trimming operations. They are very adaptable 6–axis configurations, but since there are no linear axes cutting a straight grove requires synchronized multiaxis motion; not unlike using your arm to draw a freehand line with a pencil. The video below shows a typical deburring operation.