Berber origin?
According to Beth Hatefutsoth, The Nahum Goldman Museum of the Jewish Diaspora, (P.O.B. 39359, 61392, Tel-Aviv, Israël), letter received august 3 1998 by The French Bob Cassuto part of the name is of berber origin: CASSUTO, CAPSUTO, CAFSUTO.

Many Jewish family names are linked to places of origin or residence. The three surnames in this group are based on CAFSA/GAFSA in Tunisia. The suffix—UT is of Berber origin and the suffix —O was added under Spanish and Italian influence. So the name means: coming from Cafsa.

The family name CASSUTO is documented since the mid-17th century. Distinguished bearers of the Jewish family name CASSUTO include the Italian Historian, Educator and Author, Moshe David (Umberto) CASSUTO ( 1883-1951, see below). 
These data are derived from the site of Bob and Francine Cassuto.

Another hypothesis
Another hypothesis is also based on the original spelling of CAFSUTO and takes it, that the O is added later. In old documents the name is noted in Hebrew als “Kaftsut” – – which could be understood as a substantive form of the hebrew verb “kafats” –  – which has several meanings: to close, to spring, to bounce.
In that case the name has a Hebrew origin. Most acceptable is the meaning: to close.

My fantasy pictures ancient Cassuto’s or Kafsuts as gatekeepers in Jerusalem, Hebron or why not Gafsa? Moreover there is a rumor to be found in letters of Italian Cassuto’s, written to the late George Cassuto Izn, that there once was a family coat of arms with a key.
But of course this is all pure speculation. Further research is needed.
In Holland there are several surnames which are analogue to this interpretation of Cassuto as a derivation of “kafats”: Springer, Sluiter etc.

A weak point is that the suffix “ut” points to a state: the closing, or the closedness, or the bouncing. It seems not to be an existing word nowadays, I can’t find the word Kaftsut in my dictionaries. The suffix for an active doer – a closer or bouncer – in Hebrew is “an”.
“Kaftsan” – springer, jumper – is an existing word and means: water-flea! 

Big head? 

Bob Cassuto mentions on his site: 
‘Another interpretation can be found in the dictionary recently published  in Brazil “Dicionario sefaradi de sobranomes”. The name Cassuto could find its origin in the name “Cabeçudo” meaning big head. This name was localized in Portugal, in Tavira, before 1400.’

Cassuto or Sacuto?

Lately I struck upon the suggestion, that the name Cassuto results from the inversion (metathesis) of consonants in another sephardic name: Sacuto.
Read more about a wealth of Sephardic namens on this page: www.sehardicgen.com
To me this hypothesis sounds not too plausible; it is hardly thinkable because of the considerable difference in pronounciation, which would not go unnoticed in everyday life.

Cassuto or Cassutto?

I must mention the spelling Casutto with double t. This originated from an inadvertent registration in the 19th century by my greatgrandfather or his father Juda Cassuto. So my grandfather and his children Max, Ernest and George spelled Cassutto. George Cassuto saw to a correction after having in a juridical procedure demonstrated the mistake. This took place about 1960. Max, his elder brother and my (Rob’s) father, followed him (and consequently his children Albert, Robbert and Irene), but not Ernest. So the children of the latter still spell Cassutto.