What is the meaning of 拿 in 他就拿我没办法的信念?
Adding punctuation might help. 

抱着“誓死不从，他就拿我没办法”的信念，我只有拼命挣扎，但是我错了。

拿...没办法, literally 'take ... with no solution', is an idiomatic way to say 'could do nothing about ...'.

誓死不从，他就拿我没办法 = (If I am) determined to resist to the end of my life, he could do nothing (to make me yield).

抱着...的信念 = with the idea/belief/conviction that ...

So the whole sentence goes 


  With the idea that he couldn't do anything as long as I am determined to resist, I struggled hard with every string pulled, but I was wrong.