Can I be taken to court by a guy that use to do our yard and says we now owe 600.00 which is insane! He said if I didn't pay him by Friday then he would turn it into his atty. What will then happen? I never signed anything or nothing so can he really do this?

How many times did he mow your lawn and not get paid?

He sues you, he can sue in either small claims court or the state court I your area that does civil law suits ( different names in different places)

He takes his evidence, perhaps his records of which days he mowed and what you owe the money for.

So what is the reason he says you owe.
But depends, my company came in when I got this home, and trimmed trees, did work in flower beds and hauled off yard wastes, that was nearly 400 dollars. Then at over 50 dollars a mow, it adds up fast.