Through his mistake, die (6)
I believe the answer is:
perish
'die' is the definition.
(I know that die can be written as perish)
'through his mistake' is the wordplay.
'through' becomes 'per' (I've seen this before).
'mistake' is an anagram indicator.
'his' is an anagram of '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" .)