The film's official novelisation suggests that he was simply in shock at this point and incapable of rational thought. Blood loss, a massive chest wound and coming face-to-face with a psychopath aren't things that are conducive to quick thinking.
Bozo jammed a grenade with a purple thread knotted around the pin into
the man’s mouth.
“I believe,” Bozo said, “that what doesn’t kill you—”
Bozo yanked off his mask. The manager’s eyes widened. He was looking
at another clown face, one far more disturbing than any of the masks:
white skin, green hair, a mouth horribly scarred beneath a red slash
“—simply makes you stranger,” the Joker concluded.
The scarred clown rose and strolled toward the bus, the thread
attached to the grenade unraveling from the purple lining of his
jacket. He climbed into the bus and shut the rear door, trapping the
Additionally, the grenade is large enough that it would have locked his jaw, making it (like the proverbial nut) all but impossible to spit out, especially for someone with a chest wound.
There's also the fact that from his perspective it's not that easy to see that the grenade still has the pin in. He might just be wondering why the Joker is trailing a thread without realising what it's for until it's too late.