No, but up to the DM
If you cast mending on the homunculus servant, it is not the spell that restores hit points, it is the servant's feature that restores hit points.
The mending spell is not restoring hit points
For example, if you have immunity to damage, and a spell deals that type of damage to you, it is not the spell reducing the damage, and the spell is not changed in if it deals damage or not; it is your feature, the immunity, negating the damage. It is the same here, it is not the spell healing you, it is the feature. The text of the spell and its effect remains entirely unchanged, and contains nothing about healing hit points.
The effect that heals hit points is not magical
What remains is to determine if homunculus servant's property that causes the hit point gain is magical. If so, even though the spell does not cause it, a magical effect causes it, and you would benefit. The Sage Advice Compendium provides a checklist for this:
- Is it a magic item? The effect is not a magic item, it is a property of a construct, that maybe also is a magic item. Infused objects are magic items. The servant itself however is a creature (it has s stat block), and the creatures that are transformed magic items are not considered magical (although you maybe could challenge that, as again there is no explicit rule saying they are not).
- Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description? No. The spell mentioned is mending but the servant does not create mending's effects. And as discussed above, it is not the mending spell creating a healing effect on the bonded creature.
- Is it a spell attack? No
- Is it fueled by the use of spell slots? No
- Does its description say it’s magical? No, the healing is not described as magical.
Based on this test, the effect would not be magical.
Why up to the DM?
5e is to a large extent a game of rulings over formal rules. I think the answer is that there is no explicit rule for that says a magic item cannot be a creature, or the effect of a magic item is magical. When you have to deduce what the rules might be by inferences of other, only distantly related game features, and when even consulting the SAC does not provide clarity although it explicitly treats the subject, it should be the DM's call.
It's obvious that the game is not designed to have unlimited free healing, especially not at low to mid levels. There are no healing cantrips on purpose, and the DMG advises the DM (p. 283):
A cantrip shouldn't offer healing.