Exodus 20:13 — "Thou shalt not kill."
Exodus 32:27 — "And he said unto them, Thus saith the LORD God of Israel, Put every man his sword by his side, and go in and out from gate to gate throughout the camp, and slay every man his brother, and every man his companion, and every man his neighbour."
In these two verses of Scripture God appears to forbid killing people in one instance, but in the other He seems to command it. To solve this apparent contradiction we must recognize that such apparent contradictions in the Bible are either due to a lack of or else a wrong understanding on our part or perhaps a wrong or inaccurate translation. In this case, both these elements are involved.
First, one should note that in the command we read in Exodus 20:13, the Hebrew text does not use the normal word harag for "kill" in a general sense, but rather the word ratsach for "murder". One could translate the command more accurately as, "Thou shalt not murder [commit murder]!"
When we consider other scriptures about this whole topic, it becomes evident that there are different kinds of or different categories of "killing" from God's perspective, and they are described and defined within their respective context. Not every "killing of a person" is an act of murder. The records from the Law which deal with such issues and how to rightly judge in these matters give different levels of punishments, etc for these different categories. Not every killing is to be judged in the very same way or carry the same judgemnt.
Also, "killing" is not generally forbidden by God, because for certain crimes the Law of God as given by Moses demanded "death" as a penalty! Such an act of "killing" as part of the execution of capital punishment was ordained of God as the righteous sentence for the particular crime, for example murder and also forms of idol worship were among those offenses punished by a death sentence. Those who broke God's Law regarding these matters brought upon themselves this sentence, in a sense they "earned" the death penalty as their righteous punishment. In other places we can read about God ordering His people in cases of warfare to utterly destroy the enemy and to kill them. Such an order by God was not a case of instigating a mass murder!
Exodus 23:27 describes a situation in which a large number of Israelites had commited idolatry by worshipping the golden calf. Their righteous judgement and sentence for their behavior was death, which then was executed by the Levites in the manner described here. The Levites, who executed God's judgment did not become murderers, and by their action did not violate the command of Exodus 20:13!
We must be careful to not let our feelings and what we perhaps may think of as "just" run freely and become the measure of truth when it is necessary to determine something righteously; man's means and ability to judge properly and righteously are very limited. God however is righteous! He is the righteous judge and according to His book all is judged correctly and justly. We at times get all excited and hot and bothered and think certain things according to our judgment would be totally "injust" — but we must acknowledge that our judgment, quite often based on our feelings and our sense of justice, is oftentimes in error. We can only come close to a just sentence and righteous judging by acting in accordance with God's directive as given in His Word, the Holy Scriptures. He does judge justly and righteously, and His prescribed sentence is just and deserved.
Thus, the two scriptures above are not contradicting each other, they deal with different matters. One is the command to not commit murder, the other is the command to execute God's righteous judgment on those who had brought upon themselves a sentence of death by their idolatry.