Mark on computer screen has one swearing aloud (6)
I believe the answer is:
cursor
'mark on computer screen' is the definition.
'one swearing aloud' is the wordplay.
'one swearing' becomes 'curser'.
'aloud' indicates a 'sounds like' (homophone) clue.
'curser' sounds like 'CURSOR'.
'has' acts as a link.
(Other definitions for cursor that I've seen before include "Computer arrow" , "Movable screen pointer" , "Moving indicator on computer screen" , "Computer screen marker" , "Indicator on computer monitor" .)