The 27-year-old was offered a four-match ban by compliance officer Vincent Lunny after knocking Adams to the floor while celebrating his opening goal in the 2-0 win over County last month.
Hearts had until close of business yesterday to notify the SFA of their intentions, and they let the governing body know via the players' union PFA Scotland that they will be strongly contesting the charge.
Hamill is accused of breaking disciplinary rule 201, which includes "any physical violence", through "excessive misconduct at a match by knocking Derek Adams, manager of Ross County FC, to the ground".
It is understood, however, Hearts will argue that Hamill did not intentionally crash into Adams, and they expect that they will have video evidence available to them which will support their case.
There will be a formal hearing at Hampden on May 8 where his fate will be decided.