So - "So" is from an adverb that marks the power or virtue by which one does a thing. At the beginning of a sentence, it marks a strong conclusion: "and so," "therefore."

they -- This is from the third-person, plural form of the verb.

are - The verb "is" here is the common form of "to be" in Greek. It means to have a certain characteristic or remain in a certain condition. It also equates terms or assigns characteristics.

no longer -- "No longer " is an adverb that means "no more," "no longer," "no further" and generally, "not now."

two  - The Greek word for "two" means "two" but it was also used to mean or a "couple," which is its sense here.

but  - (CW) The Greek word translated as "but" denotes an exception or simple opposition meaning "except," "yet," "rather," and "nay." It is not the common conjunction translated as "but."

one -- The Greek word translated as "one " means "one" (as opposed to other numbers), "single," and "one and the same."As in English, it can be used as a pronoun, meaning a single person.

flesh.  - The Greek word translated as "the flesh" means "flesh," "meat," and "the physical order of things" as opposed to the spiritual.

Therefore - (CW) The Greek word translated as "therefore" either emphasizes the truth of something ("certainly," "really") or it simply continues an existing narrative. This is not the word translated as "wherefore" to start the verse that more clearly means "therefore" stating a conclusion.

what  - The word translated as "what" is a demonstrative pronoun, but it often acts as a pronoun, especially a connective pronoun introducing a dependent clause. This is the object of the verb. It is neuter, singular.

missing "the"  -- (MW) The untranslated word 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. 

God - The word translated as "God" means "God" and "deity." It is introduced with an article, so "the God." Jesus often uses it this way perhaps to indicate the one God as opposed to the pagan gods.

has -- (WT) This helping verb "has " indicates that the verb is the tense indicating an action completed in the past. This is not the tense of the verb here.

joined -- "Joined together" is from a verb which means "yoke together", "harness together", "bond fast", "join together," and "pair. Its root word is a yoke used for draft animals. It is the tense meaning "at some time" past, present, or future.

together, -- This is from the prefix of the previous verb that means "together."

let  - The "let" comes from the form of the verb translated as "out asunder" which is a command in the third person, which in English, we translated as with a "let." The sense is that something must happen or, in this case, must not.

not  - (CW) The negative "not used here is the Greek negative of a subjective opinion, commands, and requests. The sense is that "you don't want" to do or "don't think" something, not that it isn't done or real. If it was a statement of fact, a different negative would be used.

one - (WW) The Greek word for "one" in the singular means "person" and "humanity" and "people" and "peoples" in the plural. However, the sense here seems to be "a man" because a man is the one who must give the divorce papers to the wife.

separate.  -- The word translated as "separate means to physically "separate," or "divide," but is also means to "separate in thought," and "distinguish."  Jesus only uses this word here and in the parallel verse in Mark. Everywhere else he uses another word to mean "divide" in the sense of severing.The word literally means "to make space between."