It depends on where you live, but the answer is generally no. It depends on the severity of the problem, but the solution may be to try to change teachers or schools. You may also want to consider an alternative school or a charter school. Please see URL below. Your school principal or the staff in the district office may also be helpful. At the district office, call the office of Educational Services.
It depends upon where you live. Most states allow it, however, you have to get a release form from the principal of the school in your district.
School boards are starting to allow more freedoms to parents because more and more parents are homeschooling due to no other option. Parents removing their kids to home school makes the public school system look worse than it already does. They'd prefer to at least keep their numbers up, even if it means bending to allow out-of-district schooling.
I found all this out when I removed my daughter from a very bad school environment - because of the teaching staff, not the kids. The principal tried to stand in the way, the teachers tried to make me feel I was "abusing" my child by cheating her out of a "real" education. Then I found support from not only home schooling families but the school board itself, who went to bat for me and demanded the teachers stop calling my home and ordered the principal to release my daughter to another district if I ever choose to put her back into school.
Check with your state dept of education. You may be able to use the NO CHILD LEFT BEHIND act. Each state has different rules about switching districts. In some school districts you can switch schools if you can document that your child is not receiving adequate education (hence the NCLB act)