Yes, provided that the spell is on the Wizard spell list.
The DMG (page 141) under the section "Activating An Item" reports (emphases mine):
SPELLS. Some magic items allow the user to cast a spell from the item. The spell is cast at the lowest possible spell level, doesn't expend any of the user's spell slots, and requires no components, unless the item's description says otherwise.
Hence you are actually casting a spell using the item and you are not using any of your slots.
The Manifest Mind feature says (emphasis mine):
Whenever you cast a wizard spell on your turn, [...]
and it does not require using a spell slot: hence, you can employ it while casting a spell from a magic item.
Pay attention that the spell cast must be on the wizard spell list: if for example your wizard has the Staff of the Swarming Insects, then they are able to cast both Giant Insect and Insect Plague, but since they are not on the Wizard spell list they cannot be cast by Manifest Mind feature.