Putting "away" after a verb

Interesting question. It means more than just a continuing action: it means "carry on with energy".

I can think of a few more examples, but all the rest are about physical activities, usually to do with building: "hammer away" ,"bang away", "saw away". Those can all be used indicatively as well ("He sawed away at the logs until the pile was gone"), but I think "ask away" would only be used as an imperative: "Ask away!".

Perhaps some less energetic actions will work: "He sewed away at the pile of cloths"; but I can't imagine "they cut away at the papers", or "she folded away at the blankets" in that sense. (In both those cases, there is another idiom which would compete in meaning: "cut away" meaning "cut parts off/out, leaving behind the part which is wanted" and "fold away" meaning "fold and put in storage".)

So, all in all, I'm quite puzzled as to which verbs will work and which won't. I'm sure that there is a connotation of energy, though.

I think "away" in this sense means "without hesitation" or "as much as you want." It can be used with any verb I suppose, e.g., "swing away" in baseball. However in many cases away is already used after a verb to mean something else, as in "run away," "give away" or "look away."

In this context, away is a synonym for freely (i.e., without restriction).

Other examples include:

Person A: I want to dance. Person B: Dance away.

Person A: I want to watch television. Person B: Watch away.

Person A: I want to eat jellybeans. Person B: Eat away.

See the pattern?