call out

It means "call" as in telephone" and "out" as the mechanic had to physically leave his office and go to your home.

That or it means to starts a fight with the mechanic. Literally, to go to the auto shop and invite the mechanic outside for a fistfight.
I'm inclined more toward NickFun's answer, but it depends on several things, not the least of which is the context. Is there any more text to go with the sentence?

The context is:
My car wouldn't start. I had to call out our local mechanic.

Definately NickFun's definition, then.