The defender is under investigation by the Conmebol's disciplinary panel, after the incident saw Cavani sent off in reaction to Jara's provocation - hosts Chile went on to win 1-0.
Mugni, 23, recreated the incident during a training session for Brazilian Serie A side Flamengo.
Mugni has been capped at U21 level for Argentina and has played 23 matches without scoring so far this season.
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