For  - The word translated as "for" introduces a reason or explanation.

this -- The word translated as "this" means "from here" or "this/that thing."

is  - -- The word translated as "this" means "from here" or "this/that thing."

my - "My" is the first-person possessive singular pronoun. This pronoun follows the noun so "of mine."  

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. 

blood  - "Blood" is from the Greek word that means "blood", "bloodshed," and "kinship." Its common double meaning of bloodshed and kinship.

of -- This word "of"  comes from the genitive case of the following word that requires the addition of a preposition in English.  The most common is the "of" of possession.

the  - - The word translated as "the" is from the Greek article, "the," (masculine, possessive form) which usually precedes a noun and, without a noun, takes the meaning of "the one."

new -- (OS) There is nothing in the Greek that can be translated as "new" in the source we use today but it does exist in the source that the KJV translators used.

testament,  - (CW) Testament" is a noun that means "a will", "a compact," and "a covenant." It does not mean "testament" in the sense of "testimony," "evidence," or proof."

which  - - The word translated as "which" is from the Greek article, "the," (masculine, possessive form) which usually precedes a noun and, without a noun, takes the meaning of "the one."

is -- This helping verb "is" indicates that the verb is passive. Helping or auxiliary verbs are needed to translate the Greek verb forms into English.

shed  - (WF) "Shed" is from a rare verb (for Christ) that means "to pour out." It is in the form of a passive participle, "being poured out." This is not an active verb, but a verbal adjective modifying "blood."

for  - - (CW) The Greek word translated as "for" means "around" when referring to a place, but, in this context, it means "about", "concerning", "on account of," and "in regard to." This is the way Christ usually uses it.

many  - - The word translated as "many" means many in number, great in power or worth, and large in size.

for  - The word translated as "for" means "into" a place, "towards" as a direction, and "for (of purpose or object)."

the -- (IW) There is nothing that can be translated as "the" in the Greek source.

remission  - "Remission" is the noun that means "letting go", "release", "discharge (from a group)", "relaxation," "divorce", "emission," and "leave of absence." While this word is rarely used by Jesus, it is the noun form of the verb he commonly uses to mean "leave" or "drop." This verb is the same word translated as "forgive" in the NT.

of -- This word "of"  comes from the genitive case of the following word that requires the addition of a preposition in English.  The most common is the "of" of possession.

sins.  - The word translated as "sin" is a form of a word that means "to fail in one's purpose", "to neglect," and "to be deprived of." It has no sense of doing malicious evil in Greek. The best English translation is "mistake," "fault," or "failure" rather than what we commonly think of as the evils of "sin." See this article for more information and context.