Perhaps you are
making the words
curvy (which I'd have thought quite a complimentary term for a woman, on the whole), curv (curve without its last letter), cur (a term of abuse, literally meaning a dog), ur (not sure exactly why this is "your with a deep, grave frown" but it's clearly in the right ballpark; perhaps the frown is of disapproval at such txtspk), and u (from I to You...).
In more detail, at Sid's request:
Left alone, I am very bad for youse.
Right here, below are certain clues.
We begin with the word SCURVY, the name of a disease that's very bad for you.
Take an axe and cut off my head
Oh, such a nasty term for a woman?
Now (S)CURVY. If you call a woman "curvy" it generally means she is pleasingly plump, but you be be suspected of just wanting to call her fat with plausible deniability.
From the rest, drop the other end
I almost become a huge bend.
CURV(Y). "Curve" with one letter missing.
From the remaining, drop my rear
You are abusing me? Oh Dear!
CUR(V). A cur is literally a dog, but it's usually used (when it's used at all) as a term of abuse for a human being.
From what is left, take off my crown
It's your with a deep, grave frown
(C)UR. "Ur" is txtspk for "your". Sid has indicated in comments that the "grave, deep frown" was just there for metre and rhyme and therefore doesn't need explaining.
Now, cut off my tail,
Oh, my identity has changed!
U(R). "U" is txtspk for "you". This riddle started out being about "I", so that's something of a change.