Are you talking about a "dumb" phone? That I would agree is a special purpose computer.

A smartphone is definitely a general purpose computer, though. The definition of a general purpose computer isn't "a computer that can do anything a typical PC can".

A proper definition would be something like "Any computer-based device that accepts different applications". It's a differentiator between things like microwaves, which are technically computers, and smartphones/laptops/PCs/tablets.