Appendix in the middle given serious cut (7)
I believe the answer is:
engrave
'cut' is the definition.
(I've seen this before)
'appendix in the middle given serious' is the wordplay.
'in the middle' indicates the central letters.
'given' is a charade indicator (letters next to each other).
'serious' becomes 'grave' (synonyms).
The central letters of 'appendix' are 'en'.
'en'+'grave'='ENGRAVE'
(Other definitions for engrave that I've seen before include "Mistakes" , "Inscribe by cutting" , "decorate with style?" , "Cut (design) into a hard surface" , "Carve into metal" .)