Does pinched nerve in neck kills pec muscles?

Theoretically: A nerve injury in the neck, of the brachial plexus, or of the pectoral nerves extending from the plexus could cause loss of function or muscle mass, but this would be pretty rare.

It can: Nerve supply comes from the nerve roots leaving at c4-5, c5-6 and c6-7. If these are severely injured you may have pectoral wasting but you should have biceps, triceps and deltoid wasting long before pecs. See a neurologist.