I'm not allowed to play Minecraft Online?

My mother forbids me to play MC Online, since it is supposedly in the online mode to kill others, in turn, I may play offline mode as I want, although there are also zombies there, I have to kill (almost 15)

So since the game is released from 6 and from then on is considered to be without hesitation I see no problem.
There's no pronounced death animation, no blood, and otherwise violence plays a much smaller role in the game than creativity.

The game is from 6 that's right. For online mode there's no USK exam. That's enough for many parents to see it as 18 and older.

I'm sorry your mother is so misguided… But that's parents. Inform themselves wrongly and then embarrass themselves in front of their children with such statements.

Try to explain to your mother what Minecraft really means in multiplayer fashion, if you know it. Otherwise… Always keep a Minecraft with single player in the background open to which you can switch over if she is looking for you. So she does not see you playing online.

Of course there's no USK exam for the multiplayer. The classic multiplayer is also the same or identical game. It's like differentiating if you play Age of Empires alone or in multiplayer xD

Oh man

I would recommend to your mother to explain what the multiplayer is. She's misinformed (she probably saw a video showing only one of the PvP game modes).

If she does not believe your statements look for things on the internet (best * old * together lets plays, where the least PvP is shown) and if she still does not believe you show her a Mc server (preferably no minigame server, because there are mostly the whole PvP game modes) eg GrieferGames.net

If she still does not believe you, just leave it. It is never good to "deceive" your own mother and secretly do something.