Yes, it is still magical
On the basis that things do only what they say, a magical item remains magical unless there is a rule stating otherwise.
The rules call out several cases where magic items do lose their magic. Here's a sampling (all citations from Dungeon Master's Guide):
Once used, a consumable item loses its magic. (pg. 141)
Once it hits a target, the ammunition is no longer magical. (pg. 150)
Once an arrow of slaying deals its extra damage to a creature, it becomes a nonmagical arrow. (pg. 152)
Doing so ends that pellet's magic. (pg. 166)
If a magic bead is removed from the necklace, that bead loses its magic. (pg. 182)
On a 1, the staff becomes a nonmagical quarterstaff. (pg. 201)
However, many items that can regain their abilities do not include this wording:
The bowl can't be used this way again until the next dawn. (p.g 156)
The cube starts with 36 charges, and it regains 1d20 expended charges daily at dawn. [...] If the cube has insufficient charges remaining, nothing happens. (pg. 156–160)
On a 1, the staff retains its +2 bonus to attack and damage roll but loses all other properties. On a 20, the staff regains 1d8 + 2 charges. (pg. 202)
Many items also call out circumstances under which they are destroyed, in which case there is no longer an item to be magical.
It sounds like your mirror is a homebrew item, in which case the DM is welcome to add a rule stating that the item is nonmagical when without crystals, but this would be a specific exception, not a general rule.