Back from class wanting swim, dash off (6)
I believe the answer is:
scrawl
'dash off' is the definition.
(dash off can mean to write quickly)
'back from class wanting swim' is the wordplay.
'back from' indicates one should take the final letters (the letter at the back of the word).
'wanting' says to put letters next to each other.
'swim' becomes 'crawl' (crawling is a kind of swimming).
The final letter of 'class' is 's'.
's'+'crawl'='SCRAWL'
(Other definitions for scrawl that I've seen before include "Scribbled writing" , "Untidy drawing" , "Crawls away from bad writing" , "Roughly put down" , "Write untidily" .)