Vases are quite sturdy. It is not possible to move them around to make matches but they will fall down the puzzle board as pieces below them are matched or destroyed.
The vases have upto three stages and can be broken either by targeting them with power-ups or letting puzzle pieces fall on them.
A power-up will deal one damage to the vase and a puzzle piece falling on top of it will also deal one damage. Three damage is needed to destroy the highest stage vase completely.