How much is a raw 14 carat blue diamond worth?

Any raw diamond can be sold to a diamond cutter for whatever the diamond cutter will pay. The price will depend on the colour and intensity of the blue, the clarity of the stone and the ability to verify that the blue colour is natural, not radiated.

When cutting a diamond about 60% of its carat weight is lost.

As a first step, best practices dictate that you take your stone to a certified gemologist and pay for an evaluation of the diamond. This document gives you more leverage when working with a diamond cutter, than if you simply approach one not in possession of the value of what you bring in to be cut.