i had a house with a mortgage. our house was torn up by the renters and forced to tear down. can i legally drop the homeowners ins. an lessen taxes?

Please talk to a real estate attorney in your area, before you do anything like this.  One place you can find qualified counsel is our website, http://attorneypages.com

I can see several potential problems here, depending on what all the circumstances are, and your lawyer will have some questions for you.  The first one is that tearing down the house seriously reduced the value of the property -- and while that's obvious, it's a problem because your mortgage balance stayed the same, and you might have some problems with the mortgage company that will make the homeowners' insurance premium small potatoes by comparison.

Homeowners' insurance doesn't just protect the house, it protects you from liability for someone who gets hurt on your land as well.  If there is debris from the house still on the property -- such as a piece of wood with a nail sticking up, in a way that someone might not be able to see it until they got hurt by it -- that would be one example of something you'd still want the insurance to be there for.  However, without the house, you should be able to get a reduced premium, since risks like fire and so forth aren't there any more.

Real estate taxes typically get set, or adjusted, once a year.  If you're not planning to rebuild right away, notify your local tax officials (your attorney can give you details), and you should have your taxes lowered the next time around.