Wikipedia: "The Act provided $1.6 billion toward investigation and prosecution of violent crimes against women, imposed automatic and mandatory restitution on those convicted, and allowed civil redress in cases prosecutors chose to leave unprosecuted. The Act also established the Office on Violence Against Women within the Department of Justice."
The bill ended at the beginning of 2013 after failing to be reauthorized during the 2012 legislative session. All of the women in the Senate (with the exception of Nebraska's Republican Senator Deb Fischer) co-sponsored the bill to be brought for a vote during this session.
Utah's own Senator Mike Lee was one of only eight senators to vote against considering the reauthorization of the Violence Against Women Act. It is likely that Lee is against added provisions that expanded the number of visas available to illegal immigrants who are victims of domestic abuse (a provision that has already been dropped), as well as provisions that protect LGBT victims of violence and Native American victims of domestic violence. However, Senator Lee is somewhat infamous for explaining away his very partisan votes with his extreme beliefs about unconstitutionality.
Lee has not spoken about his vote today, but his argument against the 2012 bill can be found here: "The Violence Against Women Act oversteps the Constitution’s rightful limits on federal power. Violent crimes are regulated and enforced almost exclusively by state governments. In fact, domestic violence is one of the few activities that the Supreme Court of the United States has specifically said Congress may not regulate under the Commerce Clause. As a matter of constitutional policy, Congress should not seek to impose rules and standards as conditions for federal funding in areas where the federal government lacks constitutional authority to regulate directly."
For ways to contact Senator Lee, look here. You can be sure I'll be sending him an email myself. If I get a response, I'll be sure to post it.