What do the stacked prepositions "away at" mean in this sentence?

My greatest privilege thrives in work that allows me to carve away at words, changing and reshaping them until they ring true.

-- Benita Porter, The Power of Words

Does the phrase mean ‘carve away words at words’: make a good shape of words with words? Or what does it mean?

Answer

I looked through COCA for collocates immediately preceding away at, writing down any phrases which I felt used away at in the same way as your quote. (This was based on my personal judgment, and another person doing the same thing might have drawn the lines elsewhere.) Since away at can be used in other ways, I checked the actual quotes for each to make sure they fit the usage I had in mind. Here's what I found:

blast away at
chew away at
chip away at
chisel away at
chomp away at
chop away at
clobber away at
cut away at

dig away at
drill away at
eat away at
gnaw away at
grind away at
hack away at
hammer away at
jackhammer away at
lick away at
melt away at

munch away at
nibble away at
peck away at
peel away at
pick away at
pound away at
rip away at
rub away at
saw away at
scrape away at

scratch away at
scrub away at
slash away at
slice away at
smash away at
snip away at
tear away at
wear away at
whack away at
wheedle away at

whittle away at

Some example sentences from COCA:

1. Romney's other rivals also worked to chip away at his lead as they fought through the Election Day media crush.


2. Instead, states kept whittling away at the trust funds, mostly by cutting unemployment insurance taxes at the behest of the business community.


3. Fear has been eating away at the foundation of the economy for a while, like the way termites eat away at the walls of a home, one bite at a time -- and then one bite and the whole wall comes down.


4. Then I notice that in the alley behind her car, a black rabbit is nibbling away at my grandma's favorite corn (that she planted herself).

In each of these sentences, we have a pattern that looks like this:

away at

The verb is an action by which the object represented by the noun phrase is gradually eroded, worn down, or reduced in some fashion. To chisel away at a block of stone is to chisel repeatedly over time, perhaps until the block of stone is in the shape you want. To nibble away at food is to nibble repeatedly over time, gradually reducing the food, perhaps until it is eaten entirely. When acid eats away at something, it's being slowly eroded and worn away, perhaps until it's entirely gone.

It's a productive pattern, and you can put just about any verb with away at which fits these semantics. Many such verbs fall into the category of eating (chew, chomp, eat, gnaw, lick, munch, nibble, peck), but more generally they fall into a category of acts which reduce a physical object in some fashion (blast, chip, chisel, chop, clobber, cut, dig, drill, grind, hack, hammer, jackhammer, melt, peel, pick, pound, rip, rub, saw, scrape, scratch, scrub, slash, slice, smash, snip, tear, wear, whack, wheedle, whittle). Since it's productive, these lists are not complete, though any verbs I left out are probably quite infrequent.

Although these constructions literally express physical acts, they're often used metaphorically. Of the four examples I gave above from COCA, examples 1-3 are all metaphorical. Only example 4 is literal.

Now that we've got a good idea of how away at works, let's take a look at your example:

My greatest privilege thrives in work that allows me to carve away at words, changing and reshaping them until they ring true.

Like chisel away at or whittle away at, the string carve away at literally expresses carving something gradually over time. It makes the reader think of a sculptor, carefully carving a block of stone, gradually turning it into a work of art. Of course, it's being used metaphorically here; there is no actual block of stone. She's carving away at words, gradually shaping them into something else. (Apparently, she's shaping them into a metaphorical bell.)