No Mutassim was with his father a few hours before they caught him. then they separated, Mutassim ran away with a huge number of bodyguards, but they were chased down by the rebels who at the time did not know they were chasing Mutassim. Gunfire erupted between the two parties, and most of Mutassims bodyguards were killed while some were arrested, one of those arrested was so scared, he asked the rebels to not kill him in return, he would tell them who the man that is running away from them is, he told them it was Mutassim Gedaffi, so they kept on chasing him, at this point only 2 other bodyguards were with him. They cornered him, and asked him to surrender, he denied that he was Mutassim and kept on fighting instead, in the end his two other bodyguards were killed, while he got wounded in the neck, when they caught him he was alive(theres a video) they put him on an ambulance but he died before reaching the hospital.
As for Saif, there are unconfirmed reports that he is hurt and being held captive in Zliten right now. He was not with his father at all.