Will my son whose disabled and receives SSI disability receive a stimulus check if I carried him on my taxes?

No he will not.  People who are claimed as dependents do not receive a stimulus check.

My son turned 18 in 2019.  He is disabled and started receiving SSI after his 18th birthday.  He received his stimulus payment.  I am doing my taxes now, do I claim him as a dependent or not?  If I do, does that mean they will take his stimulus payment?

If you claim your son as a dependent, he is not eligible for the stimulus payment.

Please read this IRS FAQ for more information.