how can breach the form i-134 affivavit of support?

The form I-134 affidavit of support obligation cannot be breached except where the person being supported passes away, leaves the U. S. permanently, becomes a U. S. citizen, enters into removal proceedings but applies for and obtains a new grant of adjustment of status based on a new affidavit of support if one is required, or has accumulated 40 quarters of earnings. I do not see how you would be able to deport your mother unless she has committed deportable offenses. I do note that under the 2013 HHS poverty guidelines, you are only obligated to support your mother for 2013 as a single person at the 125% level. The amount of obligated support would be $14,362.50 and if you can prove it, you can deduct the $13,000 that she makes from that amount.  The same principle applies to any other year in which she is making reportable income.  Please further note that the $14,362.50 amount appplies to the 48 contiguous states and D.C. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.  

The affidavit of support is a contract between you and the US Government.  But there may be a private right of action by the immigrant to enforce it against you under some circumstances.  Here's a good legal articles in a thorough analysis of the law in this area: http://www.ilw.com/articles/2006,0110-wheeler.shtm To be clear, you can't "deport" her.  Only immigration enforcement officials can do that, and their efforts in most jursidictions are focused only on foreign residents with criminal issues.