Beginning to sign, go very slowly — it’s illegible (6)
I believe the answer is:
scrawl
'it's illegible' is the definition.
(a scrawl is illegible handwriting)
'beginning to sign go very slowly' is the wordplay.
'beginning to' says to take the initial letters.
'go very slowly' becomes 'crawl' (crawl can mean to move along slowly).
The initial letter of 'sign' is 's'.
's'+'crawl'='SCRAWL'
(Other definitions for scrawl that I've seen before include "Poor handwriting" , "Scribbled writing" , "careless writing" , "Quickly pen" , "Long, maybe illegible, piece of writing" .)