I won't say I disagree with what anyone else has said here. All true stuff. I just have a different take on it.....
You can lead your life worrying about "what if...." or you can just lead your life mitigating risks when possible and accepting that everything has a certain amount of risk. Could he get injured? Sure. I guess he could. But in my experience, in almost 10 years and having had over 100 employees in that 10 years, I've only had 3 injury claims made by employees - and those were all in the landscape construction side of things. Still haven't had any injuries related to just regular maintenance. . So the chance of any given employee getting injured is relatively low to begin with.
The chance that any given employee getting a MAJOR INJURY - one worth suing you for - is really small. Sure, it could happen. But the chances are really remote.
So it many cases, I'd say it's worth the risk. But you have a unique situation in being a minor and living at home (I assume you live with your parents still???). So for most people here on Lawnsite, I'd probably say go ahead and hire the kid. If he gets injured badly and sues your ass off, oh well. That's life. You could get hit by a car tomorrow too and be paralized for the rest of your life. But does that keep you from driving? Your mower could throw a rock into some little kid's eye and their parents would sue your ass off. But does that keep you from mowing? No. So we understand that certain risks are just part of life.
But I digress, your's is a unique situation. If you were 18 or 19 and lived on your own in an appartment, you wouldn't have too much to lose. But in your case, your parents COULD have a lot too lose. And while you may be cool with accepting a certain amount of risk, you probably should NOT pass any risk onto your parents. So if you are going to hire this kid, you're going to have to find a solution that protects your parent's assets or isolates your company. There are several ways to do that.
One way to protect yourself is to incorporate your business. But that isn't an easy thing to maintain. In order to really be protected, you have to run your corporation as a totally separate entity. Books must be painstakingly kept, detailed annual reports written, no co-mingling of funds, etc. If you make a mistake on any of these things than the prosecuting attorney will "pierce the corporate veil" as they say and find that your corporation wasn't really acting as a corporation anyway. Then you are back to square one and you and parents are liable again. So I realy doubt a 15 year old has what it takes to run a corporation properly. Heck, even I, at age 34 and with 10 years biz experience, have trouble keeping up with the demands of a corporate entity. It ain't easy.
So there are probably other ways. Worker's comp. insurance would be a great start. That would totally cover almost anything except really major injuries. Worker's comp. does have limits. So if it was a big enough injury (like death) then technically the family could sue you in civil court.
Even better would be a "umbrella" insurance policy. One that is set up to take care of any injury when worker's comp. stopped. Then you'd be almost totally protected.
But is all this worth it to you - that's the question. It's not too difficult to get worker's comp. insurance and an umbrella insurance policy. But it's gonna cost you hundreds or thousands of dollars. Can you recoup that investment? Only you can answer that.
I think you and little jimmy should be ok.