Last of joint method deleting application (5)

I believe the answer is:

roach

I'm a little stuck... Click here to teach me more about this clue!

'last of joint' is the definition.
'roach' can be an answer for 'joint' (thesaurus). I am not sure about the 'last of' bit.

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for roach that I've seen before include "Historic SE county" , "Small freshwater fish related to carp" , "Trim" , "Fish of the carp family" , "Something fishy here" .)

I've seen this clue in The Guardian.

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