Oh, my yes, you've gone too far. This has become a power struggle. There should've been increasing consequences along the way. You need to find a way to make it easy for him to co-operate with you. You've both taken a very strong stand opposite each other and now it's up to you to find a way for both of you to save face.
I think I might start out with saying we've both gone too far with this. Let's start over. And then, after you've both calmed down, have a conversation together with both of you feeling safe to state your feelings about how this went wrong. Listening is the most important thing for you to do. By your listening to him he'll better be able to listen to you. The conversation has to be calm and mostly without anger. It's to be exploratory. How did we get here and how do we change this?
I think you did error by paying him even tho he didn't need to mow the lawn. This sets you up for feeling angry and used and him for feeling he doesn't need to mow to get paid. Include this in your conversation.
Appeal to his sense of fairness. You did get paid and now it's time to earn that money.
Why is he refusing to mow? Once you know that you can better deal with changing his way of thinking. Is he just not willing to do it now but will agree to do it tomorrow? Is he angry because you're angry and he doesn't understand why you're angry? Ask him questions, keeping an open mind and remaining calm.
You'll probably need to have the conversation later, say in a day or two, so as to give yourselves time to cool down. I suggest that you keep the electronics away from him while sympathizing with him about their loss. Let him know that this is extreme and that you'll have a conversation later when you're both calm about how this can be prevented in the future. Tell him you are taking away the things that keeps him busy so that he has time to mow the lawn.
You should NOT mow the lawn yourself. He has to be a part of the solution. You can have a win/win but not if you give in (give up) and mow.
I feel for you. This is a difficult age. I urge you to read up on parenting teens. I recommend the Love and Logic books. Also How to Talk so Children will Listen and How to Listen so Kids Will Talk.
At a later time, after the lawn mowing is done, I suggest that you write down the rules of the house and then include this in your conversation with your son. Get input from him. You might be surprised at how reasonable he can be with rules and consequences. Outline consequences so you both know in advance what will happen. For example with the lawn mowing. Instead of threatening him for 3 weeks, take away on electronic gizmo each day until the lawn is mowed. Be firm but calm. It's about making life reasonable and not about fighting with your son. Never argue with him. The lawn is to be mowed today or I'll take your phone so that you'll have more time to mow. Not mowed the next day. Guess you need more time. I"ll take your computer privileges. Not mowed. Guess you need more time. etc. All matter of fact and no big deal.
As to it's seeming that he doesn't care. I suggest it's bluff and a way to try to manipulate.