Are you documenting all of this? Photos, dates, written description of the incidents and the communications between teachers and yourself? Are accident/incident reports being kept track of on the part of the school?
Is the preschool through the school district, or privately owned? Privately owned and you would be speaking to the director, not the principal.
School districts have their hands tied, relatively speaking, when it comes to expelling kids with behavioral issues. I know this because my first-grade son is being bullied; when I have spoken with other educators who are familiar with school policies, they have made it clear that it is extremely difficult to get a child expelled any more. It has to be along the lines of 'brought a weapon to school' before they have the legal ability to kick a kid out.
That said, what we have done-- and what I strongly advise you to do-- is to lean hard on the school and insist that they create a *safety plan* for your child. Be clear with them that you *expect* that your child will not be continually hurt by this child and put it back on them "what are you doing to keep my child safe at school"? Because I knew that getting my son's bully removed from his class was going to be impossible, I focused on what I could, which was making sure the school knew I was holding *them* accountable for his safety.
I would exhaust that option first before any further action; if this didn't help the situation, if it IS a program run by the district, then contact the School Superintendent.
If it is a private-run facility and the director gave me that line of 'kids will be kids'... I'd be looking elsewhere. That's a crappy line for the director to offer; yes, kids will be kids, but as a former preschool teacher, I know there are ways to ensure that children who hurt others are not allowed to do so with impunity. This does mean 'extra' awareness and work for the teachers, but some proactive strategizing can help immensely. Good luck.
ETA: reading through others' responses-- I do agree that this is not bullying; I hope in telling you how we are dealing with our own issue (much older kids, seven) that you do not think I'm drawing a parallel in regard to this youngster being a bully. If his parents choose not to get him help and give good guidance, he could *become* a bully, but he's still very, very young.