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My D&D group is currently playing a campaign. It went smoothly for the first half. And then, by request, I allowed two of the current players' friends to join the campaign, all of whom have no prior experience in roleplaying game aside from what this player told them about D&D.

The few next sessions, one of them started to make me and few fellow players uncomfortable by describing explicit sexual actions. His reasoning was "because my character is chaotic evil" - even though I told him privately that one of the rules in our session zero agreement was that there would be no explicit sexual activity in this campaign.

I even took the initiative to redo the session zero so he can participate in it and so I could hear his reasoning and expectations. From my side, I explained the usual about the tone of the adventures, what I expected from players, and my restriction on "you can flirt with female NPCs to get information, and female PC can go for a little skinship if you want, but no explicit ones. Also no descriptive gore".

And from his side, he said he understood what I wanted, and as long as he can do what he expects his character to do (we did another private talk about how would he handle the story, what the "endgame" of his character is, and how does his character would die if necessary), he said that he would do his best to react accordingly. He said he doesn't mind the agreement, and wants the story to run smoothly and wants his character to have a great time.

But the very next day, he did the same thing I told him not to "because his character has nothing to do in the night before we do a long rest".

Is there any way to get around it, or should I give a possible "punishment" that have a lasting effect on his character? Or is it my fault as a DM for not being stern enough with the session zero rules?

I want to make kicking him out a last resort.

No getting around it, and no need to work with in-game punishments. In-game punishments make the problem just another part of the game, and this is more serious than that.

You've got to be blunt here: you have an agreed code you expect players to follow. If the player starts hurting your game like this, you can and should inform them that they're no longer welcome to your game if the behavior doesn't change. In other words, an ultimatum. It's one of the more difficult parts of friendship giving this kind of feedback to someone you might like otherwise, but they just have no right to make others uncomfortable like this.

If they get defensive and point out that it's their character's personality, calmly remind them that they were aware and agreed to the rules in which case a Chaotic Evil character was probably a very bad idea (as it often is). You can always offer them to have a fresh start with a new character, or retcon their current one, if the player thinks their current character is a hindrance to playing by the agreed rules.

While @kviiri's answer is probably your best bet here, it's also a bit of a nuclear option. There is a step you can take before going there, based on your description of the problem: You said,

one of them started [...] describing explicit sexual actions

You're the DM. You can, and have the authority to, put a stop to this by wielding your DM powers to fade to black and cut to a different scene. If the player starts narrating something that makes you or the other players uncomfortable, interrupt him with:

Okay, you're doing that. Meanwhile, over at the tavern...

And immediately move on with whatever's going on in the other area. Don't pause - make sure you have your narration ready, don't give the player a chance to interrupt. You will have to be very firm with the player as they're likely to do everything they can to get the scene back. You handle this by repeating, as many times as necessary:

That's happening off-screen. We're going to focus on what's happening in the tavern now.

This takes away any gratification the player gets from describing these graphic scenes. They don't get the pleasure of imagining them out loud, they don't get pleasure from watching everyone else squirm, they don't get to be in the spotlight. If the player is a reasonable person, eventually they'll get the hint and stop trying. If not, they'll likely remove themselves from your game, which also solves the problem.