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In French, (Cass or) casse. A case is a box, but a casement is an enclosure, or fort. To Quash is to smash or to beat. LL. cassare: to annihilate, or destroy; L. cassus: empty. This word is related to Caesar, and squash/quash.

Joseph Aquilina, probably the foremost expert on the Maltese language states that this name is from a Sicilian place name. This must mean Cássaro in Eastern Sicily (accent added). There are other Maltese surnames believed to be of Italian origin, but with the end vowel missing, e.g., Sant and Gatt. I'm guessing the the place name is Arabic in origin, and derives from Qasr, "fortress".
There are other theories about the name Cassar, for which see here -
http://www.searchmalta.com/surnames/cassar/index.shtml