You should contact Trenitalia directly via e-mail for the most comprehensive answers, Check out the information for disabled travelers and the assistance offered at Mestre:

http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=052ff172e719a110VgnVCM1000003f16f90aRCRD

You access all but the closest platforms by underpasses with long steps. I don't know if there are lifts. http://www.artesia.eu/italia/stazione-mestre.php indicates there is assistance available for disabled persons. There is a Best Western right across the street and the front desk people will speak English and have a lot of information about the station if you can't contatct Trenitlia. You can speak with the Best Western for free via Skype. Just go to their website.

Here's the link for disabled assistance and the Italian website says Mestre is one of the 14 stations which have it.

http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=052ff172e719a110VgnVCM1000003f16f90aRCRD

Yes, you have to climb steps to get on the train.

ellenem,

Trenitalia offers a service to disabled travelers where they can be assisted onto trains with lifts, etc. in more than 200 Italian train station, including those in Venezia, according to links posted.

I recommend that the original poster not rely on the internet, but contact Trenitalia directly to make sure the service will be available when (and if) needed, but if it is available, it is NOT true that a traveller will "have to climb steps to get on the train."

Thank you all! I will contact Trenitlia (or call the Best Western! )