How to deal with an abandoned home
Call the bank
If the home is in foreclosure or is bank-owned, the bank should have an asset management team that maintains the property, so that's where you would direct your complaints.
It could be that they're dealing with a lot of properties at the moment, but this shouldn't be as big a problem now as in 2009 and 2010 when a record number of houses were falling into foreclosure.
If all you want to do is cut that lawn, still reach out and ask for permission. Again, you don't want to get slapped for trespassing.
If you don't know the status of the home, Foreclosure.com and RealtyTrac.com keeps foreclosure information, but they charge a fee for access. A Realtor can also let you know.
Zillow.com shows foreclosure information for free if you register at the site. Typically, Zillow lists what stage of foreclosure the property's in, and the bank or attorney in charge of it.