Which one is correct out of the below two? If possible, I request that you give a justification also.
1) He is going to mingle from single.
2) He is going to mingle to single.
"From mingle to single" and "from single to mingle" are playful expressions, a kind of word-play. The grammar is incorrect but people forgive it and play along because of the rhyme and because of the nice contrast between the meanings of "mingle" and "single".
The primary sense of single is "just one" or "alone". Socially, a "single" person is someone who is unmarried or not in a committed romantic relationship.
Mingling is talking with other people, especially people you don't already know, usually at social events like parties. "Please excuse me, I must go and mingle" is a polite way to leave a conversation with one group of people, in order to go talk with other guests at the same party. The primary meaning of "mingle" is physical: it means to mix substances together, producing a new substance composed of both: the OED mentions "crushed pearls mingled with ambergris". A common expression is to say that two rivers "co-mingle" where they meet. "Mingle" is a synonym for "mix", with a stronger suggestion of combining into something new. The word "mix" is often used to describe pleasant social interaction with a variety of people at a party, just like "mingle".
"Mingle" is primarily a verb, though it can be used (unusually) as a noun, as in "I'll go and have a mingle". "Single" is an adjective, though it can also be used as a noun: "a singles party" is a party where single people can meet and mingle.
The phrase go from X to Y is a common expression, meaning to move from one place to another, as in "go from home to school", or to transform from one state to another, as in "go from hot to cold" or "go from zero to hero". In "go from hot to cold", the X and the Y are both adjectives. In "go from zero to hero", the X and Y are both nouns.
Since this phrase describes a transition, usually the "from" comes first, because it describes the earlier place or state. However, you can say "to school from home" or "to cold from hot" if you want to give extra emphasis to the new state.
The reason "from single to mingle" is incorrect is because neither the noun nor the adjective interpretations of "mingle" and "single" make sense. As a noun, "mingle" means the action of mingling, but a "single" is a single person. An action can't transform into a person; an action might cause a person to transform, but that's different. And normally, if you meant the action, you would use gerunds, like this: "from mingling to being single". In "from mingle to single", "single" is clearly meant as an adjective, but "mingle" has no prior use as an adjective, so it doesn't make literal sense here.
So, "from single to mingle" is literally nonsense, but because of the rhyme and the fact that mingling is what single people usually do in order to find a mate (in American and British cultures), people understand the phrase as a playful figure of speech.*
Neither of these phrases means "going to get married".
She went from mingle to single.
means that she stopped mingling and became satisfied with being single. This blog post says "It doesn't mean that I don't mingle with guys anymore but the fact that I stopped entertaining guys for being more than friends." If you spelled it out with correct grammar, the sentence would be "She stopped mingling and chose to remain single."
He's going from single to mingle.
means that he's been keeping to himself, but now he's starting to mingle. Mingling might lead to getting married, but mingling is no guarantee of getting married. If you rewrote the sentence literally and with correct grammar, it would be "He's going to stop keeping to himself and start mingling." Because "single" occurs with "from", though, and "go from X to Y" means to make a transition from one state to a different state, there is a clear suggestion that he intends to stop being single—that is, to enter into a committed romantic relationship, probably marriage.
Note that in "from single to mingle", to mingle is not heard as an infinitive, but it is heard as an infinitive in "starting to mingle". This is because the familiar phrase "from X to Y" is strong and distinctive, and overpowers the "to infinitive" construction, which most commonly occurs when it's introduced by another word to make some other familiar phrase, like "start to X", "want to X", "going to X", etc.
Because "from X to Y" is the usual way to describe this kind of transition, not "to Y from X," the word-play is easier to play along with in "from single to mingle" than in "to mingle from single". The ungrammaticality of "to mingle from single" is harder to ignore. It sounds a little like an attempt to form an infinitive phrase like "to mingle with artsy people", but "to mingle from single" doesn't make sense when heard that way—or at least, it requires bending English grammar to the breaking point.
In "He is going to mingle from single", a person recognizes the familiar phase "going to infinitive", as in "I'm going to mingle", before they hear "to mingle from single". So, this phrase bends ordinary grammar so far that it's hard to play along with. It sounds more like an unintentional grammatical error than intentional word-play. In speech, a listener might not understand it at all.
* The figure of speech is called catachresis, but the word "catachresis" is not well known.
There is a catch-phrase, "He is going from single to mingle."
"Single" in English can mean that a person is not married and does not have a boyfriend or girlfriend. As in, "Since Sally broke up with him, Bob is single."
"Mingle" means to mix together with other things, like you might say, "There was salt mingled with the pepper." We often use it to refer to people spending time together socially. You might say, "Bob went to the office party to mingle with his co-workers."
So, "He is going from single to mingle" means that he is changing from a state of being by himself to being with other people, normally used to say that he used to have no girlfriend but now he has a girlfriend or is actively looking for a girlfriend.
I suppose someone could switch it around and say "He is going to single from mingle" meaning that he used to have a girlfriend and now he doesn't any more.