She has a haircut the same as me是正确的.the same...as 表示“ 类似；相同”指两个东西是同种类的.
same 是形容词 后面可以跟名词它也是代词 后面可以什么也不跟
as 是关系代词 这个以后再讲.
记住same后跟名词 就行了.动名词也是名词same后跟动名词不常见.
下列句子可参考
1he is not the same man as he was before.
2.this pen is the same as mine.