Yes, but there are ways around it
You are correct in that you don't get extra saves to shake off the charmed condition. The Charm Ray is indeed a powerful means for the beholder to prevent your character from attacking it, and without intervention this effect will last for the whole fight.
As discussed in this question, while you can't attack the beholder directly or directly target it with any harmful effects, you can still support your party. To be specific, the charmed condition has the following two effects:
A charmed creature can't attack the charmer or target the charmer with harmful abilities or magical effects.
The charmer has advantage on any ability check to interact socially with the creature.
Nothing in the charmed condition prevents you from assisting your allies, be it healing them (either with spells or potions) or providing cover or doing any other task which aids your allies who happen to be fighting the beholder. You are only prevented from targeting the beholder with harmful effects (this probably includes the Help action to help your allies hit the beholder).
There is also nothing stopping you from attempting to remove the charmed condition. The spells calm emotions (2nd level), greater restoration (5th level), mind blank (8th level) and power word heal (9th level) can be used to remove or suppress the charmed condition caused by the beholder's Charm Ray mid-combat. While the latter two are likely beyond your reach, the former two should be available for a party of appropriate level to fight a beholder. You can cast these spells on yourself if you have them available, or get a friend to cast them for you, thus ending the charmed condition.
As indicated by CTWind, there exists another way to suppress the effects of the Charm Ray, and that is by using the beholder's own Antimagic Cone (or another antimagic field you happen to have handy, but we'll assume you don't have one of those). The Eye Rays are explicitly magical, and the duration of the Charm Ray's effect is not Instantaneous. Within the antimagic field...
Any active spell or other magical effect on a creature or an object in the sphere is suppressed while the creature or object is in it.
This would include the effects of the Charm Ray. The beholder's Antimagic Cone even calls out the Eye Rays as being affected by it. Thus, if you stand within the beholder's Antimagic Cone, the charmed condition is suppressed and you can attack normally.
This is not a fool-proof plan, as the beholder can move or deactivate its Antimagic Cone at the start of its turns. But in doing so you force the beholder to choose between using its Antimagic Cone to suppress your party's casters and magic items or leaving you charmed.