Does the etymology of the word "government" mean "to control the mind"?

Government comes from the term govern. From Old French governer, derived from Latin gubernare "to direct, rule, guide, govern", which is derived from the Greek kybernan (to pilot a ship).

Don't believe the nonsense you read online. There is precedent that the suffix -ment is derived from the latin mente meaning mind in some languages, particularly Old French. Words deriving from the mente sense generally have the suffix -wise or -ly, and are adverbial in nature.

But, it is also from mentum - (instrument or medium). It is this second sense that was imported into English.

In English, -ment means: the means or result of an action. Per multiple sources -ment is derived from the Latin mentum via Old French. For example, the Online Etymological Dictionary is quite clear on this subject.

In French there are two etymologically separate suffixes –ment. First there is –ment from Latin mente, the ablative of mēns “mind”. This is used in French to form adverbs from adjectives, like lentement “slowly”. Then there is –ment from Latin –mentum, which forms abstract nouns from verbs. This is not connected with the words for “mind” but derives from the Indo-European noun suffix *-men- with -t- extension, as in testamentum. French gouvernement (whence English government) belongs to the latter.

The idea to explain the English word government or the French word gouvernement with Latin/Greek gubernare to govern and Latin mens/mentis mind is ridiculous. In Latin we have a lot of words with the suffix -men: flu-ere to flow and flu-men river.

And we have a lot more words with the suffix -mentum as in funda-mentum. Nobody would dare to maintain that -mentum has something to do with mind.