This may be a duplicate based on "Do you know when you are under the effects of a charm/domination spell?".
In a recent session our group were fighting Mind Flayers and were repeatedly subject to domination spells.
As a Paladin I opted to use Cleansing Touch to end the effect of the spell on myself.
Cleansing Touch from the PHB:
You can use your action to end one spell on yourself or on one willing creature that you touch.
Our DM allowed it, based on the fact that the description for Dominate Monster doesn't explicitly state that I couldn't end the effect in such a way, but RAW should I have been able to?
Dominate Monster from the PHB:
You can use this telepathic link to issue commands to the creature while you are conscious (no action required), which it does its best to obey. You can specify a simple and general course of action, such as “Attack that creature,” “Run over there,” or “Fetch that object.” If the creature completes the order and doesn’t receive further direction from you, it defends and preserves itself to the best of its ability.
For clarification, I failed the Saving Throw and the Mind Flayer issued a general command of "Kill this PC", never assuming direct control of my character.
Best Answer
No, RAW you could not have done that
You failed your save and you got an order to kill a specific PC. Instead, you used your action doing something to break free from the dominate effect, failing to follow the command you were given.
A DM is free to allow this, but if a DM allows you to do that, dominate monster becomes essentially useless, as it sets a precedent for ignoring the order and just doing something else; expect dominated monsters to simply drop prone or drop their weapons to avoid following orders.
In fact, as pointed out in comments by Lino Frank Ciaralli, your character isn't even aware that they are being dominated. Any attempt to 'break free' would be using meta knowledge that your character has no knowledge of.