The word miseo appears 173 times between the New Testament and Septuagint. It comes from the root misos meaning "hatred." Miseo means "hate, detest, abhor." It appears 35 times in the apocryphal books.
In the Septuagint and a Hebrew translation of the New Testament I have, it is usually used for sone. If I had a copy of Hatch and Redpath's Concordance to the Septuagint, I could find a list of all the Hebrew words it translates in the Septaugint (it's one of the appendixes, and was the most useful portion of the book to me in my seminary studies).
In Brown, Driver, Briggs Lexicon, they list the meanings of sone and its permutations as "hate, hatred, abhor, detest, foe, etc." They also note that it can be used in some cases for "revulsion/repulsed." The examples they give are 2 Sam 13:15, Dt 22:13, 16; and 24:3.
2 Samuel 13:15 ¶ Then Amnon hated her with a very great hatred; for the hatred with which he hated her was greater than the love with which he had loved her. And Amnon said to her, "Get up, go away!"
Deuteronomy 22:13 ¶ "If any man takes a wife and goes in to her and then turns against her,
Deuteronomy 22:16 "The girl's father shall say to the elders, 'I gave my daughter to this man for a wife, but he turned against her;
Deuteronomy 24:3 and if the latter husband turns against her and writes her a certificate of divorce and puts it in her hand and sends her out of his house, or if the latter husband dies who took her to be his wife, [All NASU. Translations of sone bolded.]
In the Dt verses, we see that she is being turned away and divorced. In that sense she is rejected.
As far as taking a sense of "reject" from miseo, the most promising verses are the following parallel statements:
Luke 14:26 "If anyone comes to Me, and does not hate his own father and mother and wife and children and brothers and sisters, yes, and even his own life, he cannot be My disciple.
Matthew 10:37 "He who loves father or mother more than Me is not worthy of Me; and he who loves son or daughter more than Me is not worthy of Me.
I actually suspected this would be the other way around, but it looks like Luke just translates his Hebrew/Aramaic source using sone as miseo. This is actually very common in antiquity. Translators would decide on a one-to-one ratio for words and usually stick to them. For this reason, you will see the same word in a Hebrew book used in differing contexts and with differing shades of meaning all translated with the same Greek word in the Septuagint. More details can be found here.
However, Matthew smoothens it out for us. He translates Jesus' words in "love [them] more than me." There we have a Hebrew speaker understanding and applying a judicial sense to the term in question. If you had to choose between your parents and Jesus, you must reject your parents to be worthy of Jesus.