How about telling him someone else mentioned the state of your overgrown yard to you...like:
"Hey Joe Mower Guy - Someone mentioned to me that my grass was getting tall, and I realized for my business it might be a good idea to have my lawn mowed once a week - or at least every 10 days, like 'Mr. Former Guy Who Recommended You' did. I can afford to pay $30 (insert your number) a week if you can give me once-a-week service. I know you're busy, so if you don't think this schedule will work out for you, do you think 'Mr. Former Guy Who Recommended You' knows anyone else who'll be able to come every week?"
This approach puts the ball in his court, isn't really confrontational (you're just passing on information), and it lets him know that you are ready to call someone else. If you don't already, you might pay weekly instead of monthly if you can, so you're not out the money if he doesn't show up.
By the way, dblreedr, I just wanted to let you know I think your grass is overgrown, and it would probably be a good idea for you to get it mowed more often. (There - no lies!)