I think the meaning of this sentence will depend a lot on context, as Rena says. It's hard to guess what it means without knowing more about the circumstances. It might be a variation on the phrase "going away at it," which is a sort of slang term that means you're focused on something and working hard on it. For instance, you could say, "John must be in a hurry to finish that painting. He's been sitting there just going away at it all day, without even taking a break." Or you could say, "This homework assignment is really hard. I've been going away at it for three hours, and I'm still not finished." I'm not sure that's what this sentence means, though. More context might help to make it clear.

It is not clear what 'going away on it" means without any context. Can you tell us more? What came before that sentence?