Trump called Clinton a "nasty woman" during the last of three debates after Clinton made a disparaging remark about him. He meant it in the negative sense. Nasty in terms of distasteful. In this context, it did not have any sexual connotations.

However, in the idiomatic sense, many "negative" words have been adopted to mean the exact opposite. Words like "bad", "ill", "sick", "retarded", "nasty" have been used to describe things that are "really good", "impressive", "highly unusual", "skillful".

"Nasty woman" was co-opted by many women to describe a strong and assertive woman who doesn't bend to a man's will. They where the term as a badge of honor.

One of the most notable women to have done so is Janet Jackson. She wrote a song called Nasty Girl. The song has become an anthem for the "Nasty Women" after Trump's comment went viral.

If you look here in the Urban Dictionary http://www.urbandictionary.com/define.php?term=nasty  at several people´s definitions, you will see  the ¨top¨ one is the most common, but in many slang ways nasty has positive connotations.  

I am not sure which Trump speech you are referring to, but in his campaign Trump made many, many offensive remarks about women.  Many people regard him as a misogynist, someone who devalues women.  Perhaps you are referring to this comment about Hillary being a nasty woman?   https://www.washingtonpost.com/news/the-fix/wp/2016/10/20/trumps-such-a-nasty-woman-comment-has-sparked-something/