Is there a way to clip the Google Satellite Layer from OpenLayers plugin?

Googles terms of uses forbid saving, reprocessing or creation of derivative work of google maps data and this is why there is no option to save the Google layer in QGis.

If you don't care about that ( private noncommercial project, studying, no redistribution, ...), then there are two options:

• You simply create a new polygon layer in QGis, make it editable and digitize your buildings or area of New York State.
• You can get a georeferenced raster using Project | Save as Image ...

However, i would advise you to look for other free available sources or purchase your own satellite images!

Alternatively you could find Imagery here http://gis.ny.gov/gateway/mg/