I had nothing to do with this

就是:I had nothing to do with this = 这件事与我无关 = I didn't take part in this = 这件事我没有参加; (I didn't have a hand in this, they did it without my knowledge 的含义呢)

do with 常与连接代词 what 连用，而 deal with 常与连接副词 how 连用，如：
1 . I don’t know how they deal with the problem . (= I don‘t know what they do with the problem . )我不知道他们如何处理这个问题。
2 . He is easy to deal with . (= He is easy to do with . 这时“do”是不及物动词)他是容易相处的人。这两个词组在使用时有细微的差别。一般地说，do with 表示“处置”、“忍受”、“相处”、“有关”等。如：
1 . They found a way to do with the elephant . 他们找到对付那头大象的办法了。
2 . We can’t do with such carelessness . 我们不能容忍这种粗枝大叶的作风。
3 . We are difficult to do with the new comer . 我们很难与新来的那个人相处。
4 . I have nothing to do with him . 我跟他无任何关系。

deal with 意义很广，常表示“对付”、“应付”、“处理”、“安排”、“论述”、“涉及”等。如：
1 . They could properly deal with all kinds of situations . 他能恰当地应付各种局面。
2 . Deal with a man as he deals with you . 以其人之道，还治其人之身。
3 . This is a book dealing with Asian problems . 这