This doctrine is based on two verses that Allah allegedly instructed Mohammed to put into the Quran.
"None of Our revelations do We abrogate or cause to be forgotten, but We substitute something better or similar: Knowest thou not that Allah Hath power over all things?" Surah 2: 106
"When We substitute one revelation for another, and Allah knows best what He reveals (in stages), they say, 'Thou art but a forger:' but most of them understand not." Surah 16:101
The documentation for the information that I am offering in this piece is found in one of Islam's classical reference books in the Arabic language. It is titled "al-Nasikh wal-Mansoukh" (The Abrogator and the Abrogated) and was authored by the revered Muslim scholar Abil-Kasim Hibat-Allah Ibn-Salama Abi-Nasr. The book goes through every Surah (chapter) in the Quran and cites in great detail every verse that was cancelled-out/overridden by particular verses that were written later. The author noted that out of 114 Surahs (chapters) of the Quran, there are only 43 Surahs that were not affected by this concept. The implications are very revealing. It means that those who would be inclined to accept the Quran as reliable can take only 43 chapters of the Quran at face value. The majority of its chapters cannot be taken at face value. The cancelled verses are mixed in with the authoritative verses and only schooled Islamist know which is which.
Read the whole, fascinating story of abrogation.