I can't express the rage that your post gives me OP. Not directed at you, of course, but the BLOODY STUPID SATS. Absolutely ridiculous, pointless tests, sucking the joy out of education (and Year 6 in particular). Please tell your son from me (a teacher) that he is NOT STUPID, the cartoon by the previous poster posted is perfect. SATS test a specific, narrowly defined area. My friend's daughter is a talented artist, her SATS were fine but would anyone who looked at them know that, NO! Another friend's son is brilliant at drama (stole the show at the end of year play), his SATS pegged him as below average. SATS only tell you a tiddly bit about a person. Like looking at a picture of just someone's ear and declaring the person to be beautiful or ugly.
So specifically to your son, tell him over half the children in the country were the same as him in not reaching the 100 mark. Simplify it to 'if there were 10 children in this room right now, 5 of them would have got less than 100' - not because he can't grasp the first statistic but it's easier for children to think in real terms. Find the things he is good at and do those! Whether it be drama, art, singing, trampolining, cycling, whatever! What other posters have said about secondary being a fresh start. Also, there are so many more teachers, subjects and opportunities at secondary, he'll find his place to shine.
I wouldn't go down the tutor route now but are his dyslexic needs being met? If he is on the spectrum of dyslexia was he receiving much intervention/support? I would make an appointment to see the SENCO at his new school in the first week. Make sure they know about his dyslexia and that his teachers do. Ask if they will be providing things he might need eg coloured sheets, ask what they will expect you to do at home, how much support you will be expected to give with homework etc.
Good luck to you and your son and have a great summer!