Beat by pushing endlessly around (6)
I believe the answer is:
punish
'beat' is the definition.
(I've seen this before)
'pushing endlessly around' is the wordplay.
'endlessly' means to remove the last letter.
'around' is an anagram indicator.
'pushing' with its final letter taken off is 'pushin'.
'pushin' with letters rearranged gives 'PUNISH'.
'by' is the link.
(Other definitions for punish that I've seen before include "Fine perhaps" , "Flog" , "Fine maybe" , "exact retribution" , "Cause to suffer for an offence" .)