請問[has Susan]是省略了什麼？感謝！ ?

She's got a way with her, has Susan.
= Susan has indeed got a way with her.

[has Susan] or [Susan has, 較正宗的寫法] 這是一種陳述句標籤(statement tags), 作用是強調或加強句子的肯定性。 句子並沒有省略什麼!

***Note***
1. "Susan" as appeared at the end of sentence, is a kind of "tail construction" referring back to the sentence subject, the pronoun "She".  
2. Mrs. Medlock was not asking a question, either for verification (balance tag) or ironic (unbalanced tag) purposes, in her statement about Susan. The punctuation was correct as it stood!  It is not a tag question!