The version in Matthew 26:39 is a request of God, but though translated similarly the key verb here is not a request.  Nor is "remove" a good translation of the uncommon verb involved. This translation makes this verse sound more like Matthew, which uses a different verb. It is worth pointing out that, since Jesus was alone, either someone overheard this prayer or he related it to someone before his death. Otherwise it could not have been recorded.

"Father" is the Greek noun that means "father" or any male ancestor so "forefathers". It is the word that Christ uses to address his own Father. 

The "if" here expresses a condition but it means nothing regarding whether that condition is met or not. It also means "if ever" and "whenever."

"Thou be willing, " is a Greek verb that means "to will", "to wish," and "to prefer." It is an uncommon word. There is a common verb that means to "want" or "desire". Jesus uses the noun form of it later in this verse, so this word was chosen for a specific reason.  It has a sense of "prefer" which the more common word does not have.  The form is passive, "is preferred". The form of possibility is dictated by the "if" that begins the verse.

"Remove" is another very uncommon word, which means "bring to", "bring forward", "carry past", "hand over", "turn aside", "turn towards",  "mislead", "change/later" (a decree), "sweep away" (a river), "let pass", or "differ" (in dialects). None of these really mean "remove".  Literally, the word means  "bring by" or "bring aside". It is not a command, as translated but an active verb, "it brings by" or "this brings by".

 "This" is a demonstrative pronoun that means "this", "here", "the nearer," and "the familiar." The form could be either the subject or the object of the verb. So, "this brings aside the cup from me"

The word for "cup" means "a drinking-cup", "a wine-cup", "a jar," and "a receptacle" for offerings in the temple. The cup is used by Jesus as a symbol for sharing burdens. See this article for more. It has an article, so "the cup". The form could be either the subject or the object of the verb.

The word translated as "from" means "from" in both location and when referring to a source.

"Me" is the regular first-person pronoun in Greek in the possessive form, so "my" or "of me".

The word translated as "nevertheless" is a less common preposition used like a conjunction that means "except", "save", "besides," and "in addition to."

The negative used here is the Greek negative of a subjective opinion, commands, and requests. The sense is that "you don't want" to do something, not that it isn't done or don't think something that might be true. Since the topic is "will", this is the right negative.

"My" is the Greek equivalent of our first-person possessive singular pronoun. 

The word translated as "will" means what someone wants or desires as well as the "will" of character. It mostly means what one wishes or has determined shall be done. It also means a desire or a choice. When applied to people, "desires" works, but when applied to God, the concept "purpose" seems closer to Christ's usage.  The verb form of this word is the word commonly translated as the verb "will" in Jesus's words.

The Greek word translated as "but" denotes an exception or simple opposition. It is used to emphasize the contrast between things like we use "rather". It is the Greek word "other" like we use "otherwise".

"Thine" is two Greek words meaning "that of mine". It consists of and article and the pronoun.

The word translated as "be done." means "to become," that is, to enter into a new state. In Greek, especially as used by Jesus, it is the opposite of "being," which is existence in the current state.  It is not the verb usually translated as "done" in the Gospels. This is in the form of a command or request. The form is passive, so, "come into being."