If you went to work for a full day of desk work and then came home to a pile of paperwork from your boss, would you tune out and be sick of it?
Your child spends 7 hours a day in school, and he comes home to worksheets? Maybe he's trying to get it out of the way so he's just throwing down some nonsense answers or tuning out entirely!
So what's your goal? Are you totally focused on academic skills, based on regurgitating information like addition/subtraction facts or spelling words? What about other things to develop his brain - like free play, creative arts, nature walks, building with blocks and figuring things out (structure, support, etc.), combining items from different play sets in new and fun ways, flying a kite, making bird feeders out of pine cones/peanut butter/seed, developing gross motor skills by riding a bike or throwing a frisbee with you, figuring out how to fly a kite, making an ant farm or looking at caterpillars through a magnifying glass....get the idea?
Maybe there's nothing wrong with his brain. Maybe there's something off in your approach and your insistence on a certain method of teaching.
He's 7. He needs to play, to develop social skills, to have down time, to just be a kid rather than a student all the time. Being a "student of life" is so important! No child does well in high school, college, or the working world if all he can do is sit and fill out papers. Let him be his full and complete self! You are just as good a mother - even better, actually - if you take your child on a nature walk with a bucket to pick up cool stuff and let him come home where maybe he decides to wash, dry and paint some rocks to give as paperweights to Grandma and Uncle Josh. Or maybe he doesn't - he just builds a mini rock wall and then breaks it down a day later to build something else.
If he has problems at school with focus and attention, the teacher will let you know, either by email or during a conference. If he needs services, he can get them from skilled educators and psychologists during the school day. But you're not saying anything along those lines. And even if he did need specialized help, it doesn't change the fact that he needs play time and down time and fun reading (no one correcting his words) at home.