wouldyoumindnotopenthedoor？为什么不能用dont？要怎么区分它们？
首先，更正一下：Would you mind not open the door？ 这一句话是有误的。正确的应该如下：
Would you mind not opening the door？
以下是Would you mind 用法小结：
一、Would you mind 的用法有如下几种情形：
1、Would you mind + doing.
例：Would you mind closing the door? It's cold outside.
你介意(你去)把窗户关一下吗?外面很冷。
2、Would you mind + 代词词宾格/形容词性物主代词 + doing.
例：Would you mind me/my smoking here?
你介意（我）在这里抽烟吗？
Would you mind me/my opening the window?
你介意（我）开窗户吗？
3、Would you mind + if 从句。
例：Would you mind if I smoke here?
你介意我在这里抽烟吗？
4. Would you mind not doing sth?
请（对方）不要做某事好吗?
Would you mind not smoking here?
请（你）不要在这里抽烟好吗？
5. Would you mind 句型一般用在面对陌生人时或者非常正式的场合,用来表达委婉、客气 的意愿。应该是 Would you mind me doing sth 或者 Would you mind my doing sth （语义稍有差别。前者表达不一定马上就行动,后者表达你不介意的话,我马上就行动。）
6. Would you mind I doing sth 是错句
Would you mind if I doing sth 改为 would you mind if I do sth 就对了。
二、Would you mind 的回答问题
若表示“不介意”或“同意”时，常用否定形式。如：
1. Would you mind doing sth?
① Of course not. I will do it.
② Certainly not. I will do it.
③ Not at all. I will do it.
2. Would you mind me/my doing sth?
① It doesn't matter, please do it.
② Never mind, please do it.
③ No, go head.
④ No, please do it.
3. Would you mind not doing sth?
① Sorry, I won't do it again.
② Sorry, I will ....
若表示“介意”或“不同意”时，则常用较委婉的方式加以拒绝。如：
① I'm sorry but I ...
② Sorry, you'd better not.
③ I'm afraid you can't.
④ I wish you wouldn't ...
⑤ I'm sorry, but it's not allowed ...
mind 和 open 是两个动词 不能同时出现在句子中 因此要把后者改为动名词形式