I’ve been building themes for 4 years and from my experience build the design provided by your graphical designer from scratch would be better solution. It helps you understanding the whole structure of your theme.
Also modifying existing theme to suit your new design can take longer time, since you’re required to learn the basic structure of the theme and all of the codes and functionality.
I would use existing theme as a guideline for creating my own theme when working with some PHP codes.