I think it's because for one, they don't know of that possibility and probably wouldn't want to risk it. Also his main priority is finding Clem, having his arm cut off and healed, along with the chance of dying, would take too much time; he doesn't know where Clementine is, and he doesn't want to waste a second.
Secondly, if they were to think of that possibility now, that they could cut his arm off, it's probably too far now. The infection has spread to much into his bloodstream that it's impossible to stop now.
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