And hold fast, all together, by the rope which Allah [stretches out for you], and be not divided among yourselves; and remember with gratitude Allah’s favour on you; for ye were enemies and He joined your hearts in love, so that by His Grace, ye became brethren; and ye were on the brink of the pit of Fire, and He saved you from it. Thus doth Allah make His Signs clear to you: That ye may be guided. (3:103)

God mentions not to get divided and follow the last book revealed by Him.

There is among them a section who distort the Book with their tongues: [As they read] you would think it is a part of the Book, but it is no part of the Book; and they say, “That is from Allah,” but it is not from Allah: It is they who tell a lie against Allah, and [well] they know it! (3:78)

When people say something is from God or His messenger. Make sure it came from the Quran before you believe it. God is pointing out to the people who are misinterpreting the Quran and then preaching it.

As for those who divide their religion and break up into sects, thou hast no part in them in the least: their affair is with Allah: He will in the end tell them the truth of all that they did. (6:159)

Prophet Mohammed did not command any person to break up into sections or groups. Mohammed is not responsible for this. God tells Prophet Mohammed not to worry and God will handle the people who split.

The English word for Shia is sect. The meaning of sect is a group and there are plenty of sects in Islam.
This verse is saying all sects are forbidden in Islam. This means religion should not be broken up into the various sects such as Shia, Sunni, Shafi, Hanafi, Maliki, Hambali, Salafi, etc. It does not matter what the sect is called, the point is that God did not authorise the sect. Islam is one religion and all people should follow the same rules mentioned in the Quran.

Turn ye back in repentance to Him, and fear Him: establish regular prayers, and be not ye among those who join gods with Allah,- (30:31)

The word joining the two verses can be ‘like’ or ‘or’ depending on the translater. Regardless of the joining word, it brings about the same meaning.

Those who split up their Religion, and become [mere] Sects,- each party rejoicing in that which is with itself! (30:32)

Breaking up into sects is the same as joining other gods with God Almighty. All sects should be rejected as it was created years after the death of the Prophet Mohammed.

Then shall We certainly drag out from every sect all those who were worst in obstinate rebellion against [Allah] Most Gracious. (19:69)

Truly Pharaoh elated himself in the land and broke up its people into sections, depressing a small group among them: their sons he slew, but he kept alive their females: for he was indeed a maker of mischief. (28:4)

God gives an example for what had happened during Ancient Egypt. Pharoah who was a very evil person broke the people up into sects. The same people who in this age who agree to divide the Muslims in different groups are also evil people.

The same religion has He established for you as that which He enjoined on Noah - the which We have sent by inspiration to thee - and that which We enjoined on Abraham, Moses, and Jesus: Namely, that ye should remain steadfast in religion, and make no divisions therein: to those who worship other things than Allah, hard is the [way] to which thou callest them. Allah chooses to Himself those whom He pleases, and guides to Himself those who turn [to Him]. (42:13)

God mentions the same religion that was sent to Abraham, Moses, Jesus, Noah and others should not be divided. This verse implies being part of a sect is the same as worshipping an entity other than God.

Islam laws are based on two sources which are God and His Messenger. People should listen to Imams who only preach from the final book of God.