This verse has only one active verb, the rest are added in the KJV. This statement is another good example the difference between a spoken phrase, which isn't necessarily grammatically complete and a written sentence. There are two different conjunctions translated as the same word. There is one unique word for Jesus in it.

The Greek word translated as "but" means "but", "however", and "on the other hand". It joins phrases in an adversarial way. Since it always falls in the second position, translating it as "however" often captures its feeling better.  

The pronoun "you" is used explicitly as the subject of the sentence. Since it is already part of the verb, its use here creates emphasis on the "you" as we might say "you yourselves." It is plural.

There is no verb "shall...be" in the sentence.

The Greek word translated as "not" is the Greek negative used to deny objective facts, not opinions. It makes a negative statement of fact. Adding "really" to the sentence captures the same idea.

The word translated in KJV as "so" is in its adverbial form, so it means "in this manner" or "in this way."

The Greek word translated as "but" denotes an exception or simple opposition. It is not the same word that is the "but" at the beginning. There a It is used to emphasize the contrast between things like we use "rather". It is the Greek word "other" like we use "otherwise".

There is no "he that" in the Greek.

"The greatest" is an adjective which is the comparative form of the word meaning "big" or "great." It means "bigger", "higher", "longer", "greater" and simply, "superior." When it is introduced by an article, it means "the greater." It is not the superlative form, "the greatest" but the comparative, "the greater".

The word translated as "among" also means "within", "with," or "among."

The "you" here is plural, indicating many of Christ's listeners.

The word translated as "let him be" means "to become," that is, to enter into a new state. In Greek, especially as used by Jesus, it is the opposite of "to be," which is existence in the current state. The form is a third-person command, which is indicated by the "let him". The voice is a middle passive, someone being acted upon by himself, but our word "becomes" has that sense without adding anything to it.

The word translated as "as" is a word that as an adverb/conjunction means "thus", "as", "how", "when", "where", "like", "just as", "so far as", "as much as can be", "that", "in order that", "nearly (with numbers)," and "know that." However, the form could also be a pronoun, "this one" or "that one" as an object.

"The younger" is the comparative form of the adjective that means "young", "youthful", "suited to a youth", "new", "fresh". It is introduced by an article so it acts like a noun, "the young one" or "the new one".

The Greek word translated as "and" is used as the conjunction "and", but it also is used to add emphasis ("also").

The word translated as "he that " is the Greek definite article, which usually precedes a noun and, without a noun, takes the meaning of "the one." The Greek article is much closer to our demonstrative pronouns ("this", "that", "these", "those"). See this article for more. Here, it comes before an adjective form of a verb.

There is no "is"  in the Greek.

"Chief" is the unique word here, one that Jesus only uses once in the Gospels. It is a verb that means to " go before, lead the way, be a leader, "lead", "command", "rule", "have dominion", "believe", and "hold." It is in the form of an adjective, "leading".

The word translated as "as" is a word that as an adverb/conjunction means "thus", "as", "how", "when", "where", "like", "just as", "so far as", "as much as can be", "that", "in order that", "nearly (with numbers)," and "know that." However, the form could also be a pronoun, "this one" or "that one" as an object.

The word translated as "he that" is the Greek definite article, which usually precedes a noun and, without a noun, takes the meaning of "the one." The Greek article is much closer to our demonstrative pronouns ("this", "that", "these", "those"). See this article for more. 

The Greek verb translated as "doth serve" means "to act as a servant", "to minister," and "to perform services." It is usually translated as "minister". It is from the same root as the Greek word usually translated as "minister".  However, in English, the word  might be better translated as "helper" though this word does include ideas such as "serving" a meal. It is not an active verb, but a verb in the form of an adjective, "serving", so with the article, "the one serving". However, this word doesn't refer to the idea of serving a meal.