Process for making rock, a fatal day used up thinking (13)
I believe the answer is:
sedimentation
'process for making rock' is the definition.
(as in sedimentary rock)
'a fatal day used up thinking' is the wordplay.
'a fatal day' becomes 'ides' (Julius Caesar was killed on the ides of March).
'used up' is a reversal indicator (in a down clue, letters go up).
'thinking' becomes 'mentation' (mental activity).
'ides' in reverse letter order is 'sedi'.
'sedi'+'mentation'='SEDIMENTATION'
(Another definition for sedimentation that I've seen is " Process of depositing".)