The venetian lagoon relies on the tidal flushes to remove the sewage from it. Add that to the fact most canals are only 3m or so deep and very narrow its not a place to want to dive.
Another issue there is you wont have a car so transporting dive kit to a boat is a little difficult.
I dont think shore diving off the Lido in the adriatic side is going to be that exciting either as its basically a gentle sloping sandy bottom.
There must be some wrecks out there though and dive charters running if not from Venice itself but maybe from Lido or the areas on the mainland to the north.
A few hotels in Venice have "scuba diving" listed as a recreation but the only diving centre i can find listed with a Venezia address is here:
http://www.bluesport.net/ . Looking on a map this is located in a marine via one of the exits from the lagoon east of the Lido in the town of Veneto so it maybe worth contacting.
A google for Venezia Italia Scuba turned up a few other possibles here:
http://www.dive-rite.com/dealers/tek/ (in the hotel excelsior).
"Sea Noble Service. Via Casati 15, Venezia, VE, Italy 30175, Veneto, Tel: +39-348-8125069 Fax: +39-041-5380614" also turned up and again its in Veneto near a lagoon entrance.
Also see
http://www.serenissimadiving.com/ which is on the south mainland side of the lagoon. Looks like there are a few options but as expected none really in the city itself.
Id be interested in the answer to this as visit venice quite often but not considered diving there.