Is it legal to ask for my daughter to be withdrawn from school because she used a foul word in a conversation with a dean? 

You are presumably paying to send your daughter to school, correct? In that case, unless the situation below applies (see below) the school is violating its contract with you--you paid tuition, they agreed to educate your daughter. You could sue if necessary to force reinstatement and/or get damages--such as damages resulting from impacting your daughter's preparation for college.

The possible hitch: what does it say in any documents from the school (e.g. the contract or agreement) with them, or any documents incorporated by reference (such as a code of conduct, if the tuition, etc. agreements say that students will be subject to the code of conduct). If there is a written agreement or policy that a student my be suspended or expelled for profanity; for insulting a staff member; or at dean's option, then the school is within their rights to exclude her. You may be able to still get the balance of tuition back if they are not schooling her, but you could not sue for reinstatement or damages.

What about public school? Public schools must take the children of residents.