Séraphine is either scraping off a layer of paint, or is employing the sgraffito technique, per J.R.'s helpful suggestion (also see the comments below for stangdon's suggestion). In the context, this is not that important whether she is painting or scraping: the author wants to stress that she is preoccupied with her work.
The word away is used to indicate that she is doing this in a continuous manner. In the context, this serves to underscore how she is paying little attention to what goes on around her (the German invasion).
From Macmillan's definition for away:
away (6) [USUALLY PROGRESSIVE] - used for showing that someone does something continuously or for a long time:
Molly was at her desk working away as usual.
The children were all chattering away happily.
The preposition at is used to indicate the object (task, goal) to which the person's efforts are being applied:
Lily, in the early stages of being with child, often spent her days toiling away at decorating their home in preparation for many happy years ahead, and comforting her rapidly indisposed father. (Google Books)
See, the word away is not used to indicate that she is taking a layer of paint away. If she were not scraping but applying a layer of paint, we could still use away:
When the German army rumbles into town, Provost shows Séraphine dabbing away at her canvas, her hymns replaced by the thunder of mortars while Uhde, the "dirty German", is forced to flee.
Example of usage:
Once I'm dabbing away with my brush I'm like a boy making love for the first time all over again. An intense relationship is built up between the canvas and me. (Google Books, 2015)