Press finally has to cut its sarky writers (8)

'sarky writers' is the definition.
'ironists' can be an answer for 'writers' (I have seen 'satirical writers' mean 'ironists' so perhaps 'writers' could also mean 'ironists'). I am unsure of the 'sarky' bit.

'press finally has to cut its' is the wordplay.
'press' becomes 'iron' (ironing is a kind of pressing).
'finally' indicates one should take the final letters.
'to cut' means one lot of letters goes inside another (some letters cut their way into a word).
The last letter of 'has' is 's'.
's' put within 'its' is 'ists'.
'iron'+'ists'='IRONISTS'

Can you help me to learn more?