In the original script (as reflected in the film's junior novelisation) it would appear that the ship was much farther away, requiring a run of several minutes through the maze of the catacombs. A man in Saw's condition, hobbled and incapable of fast movement, would have been a massive liability to Jyn's escape, something that he clearly recognised.
Obviously, in the film itself his decision is less explicable given that they practically land the ship on his doorstep.
Jyn stood up but hesitated. She took Saw’s arm as if she planned to haul the man along with them. He shook her off, though, and Cassian could see why.
He was slow, beaten, sick. No longer the legendary warrior—the terror of the Empire—he’d once been. He wasn’t able to run any longer, but he wanted to make sure Jyn did.
“Save yourself. Please!”
“Come on,” Cassian said as he took her by the hand. She resisted him, not willing to abandon the old man who Cassian knew had once treated her like his daughter.
“Go!” Saw shouted, insisting even harder. This was his final wish, and he wanted nothing more than for her to grant it.
Cassian could see she wanted to argue with Saw, but the entire place was about to come down around their ears. It wasn’t like they could throw a grown man in armor over their shoulders and still escape. “There’s no time!”
Jyn didn’t know the layout of Saw’s hideout well enough to decide
which way to run. Fortunately, Cassian seemed to have a better sense
She chased him through the place’s empty corridors. Everyone else—all
the other prisoners and even the rest of Saw’s rebels—seemed to have
left already. They’d been able to see what was about to happen to
Jedha, and they hadn’t been worried about leaving a father figure to
Rogue One: A Star Wars Story – A Junior Novel