Yes, magic items can be destroyed.
The DMG has this to say about damaging magical items:
Most magic items are objects of extraordinary craftsmanship. Thanks to a combination of careful crafting and magical reinforcement, a magic item is at least as durable as a nonmagical item of its kind. Most magic items, other than potions and scrolls, have resistance to all damage. Artifacts are practically indestructible, requiring extraordinary measures to destroy.
So a magical net would generally have resistance to all damage, but would still come under the normal rules for nets, and could be destroyed by dealing 5 slashing damage (after its resistance was taken into account).
Note that these are just the baseline rules - all of this is up to your DM to determine, especially since a magical net is probably, although not necessarily, a homebrew item.