Marking zero — that's heartless! (6)
I believe the answer is:
noting
'marking' is the definition.
('note' can be a synonym of 'mark')
'zero that's heartless' is the wordplay.
'zero' becomes 'nothing' (synonyms).
'that's heartless' suggests removing the centre.
'nothing' with its centre taken out is 'NOTING'.
(Other definitions for noting that I've seen before include "Making brief record of something" , "Recording in writing" , "Observing or taking down" , "Seeing" , "Making brief record as memory aid" .)