Not at all insignificant person starts late, extremely angry (2,2,3)
I believe the answer is:
in no way
'not at all' is the definition.
(synonyms)
'insignificant person starts late extremely angry' is the wordplay.
'insignificant person' becomes 'minnow' (minnow can figuratively mean an unimportant person).
'starts late' means to remove the first letter (the word begins later than normal).
'extremely' says to hollow out the word (remove centre letters) (only the extremes of the word are used).
'angry' with its middle removed is 'ay'.
'minnow' with its first letter taken off is 'innow'.
'innow'+'ay'='IN NO WAY'
(Another definition for in no way that I've seen is " Not at all".)