Through his mistake, die (6)
I believe the answer is:
perish
'die' is the definition.
(synonyms)
'through his mistake' is the wordplay.
'through' becomes 'per' ('per' can mean through or by means of).
'mistake' indicates an anagram.
'his' anagrammed gives 'ish'.
'per'+'ish'='PERISH'
(Other definitions for perish that I've seen before include "Expire" , "Die; decay" , "Suffer complete ruin or destruction" , "Waste away" , "come to grief" .)