So I was doing a nice playtrough, and got this breaktrough: "Capturing asteroids". Awesome, as I am not being very lucky with the spawn rate of those. Basically, what it does is that it cancels the limted time to mine it if you land an asteroid lander...

The problem is that after the first asteroid I landed in, I noticed that the timer doesn't go back if I leave the asteroid (with my lander).

Now it is fine, but I can quickly see my hotbar full of depleted asteroids in a few hours. There is no way of removing them, Probably the game performance will suffer too in the long run.

Is there any way of getting rid of the unwanted asteroids when you have this tech? do they go away when resources are depleted by their own?

The "Capture Asteroid" breakthrough does not just "cancel the limited time to mine" in the kind of game mechanics way you are thinking of. It simulates herding the asteroid into a Mars orbit. So it is available FOREVER, until you send it away.

There are some asteroids, combinded with certain technologies, that you literally will NEVER want to send away.

But, in the ordinary case, when you are done pulling stuff from a particular asteroid, you use the Abandon Asteroid button on the asteroid's pull down that you get from the Planetary Options menu (the menu that you use to select neighbors to talk to, or remote mission to fly to).

Also, you don't have to worry about a stack of tagged asteroids confusing you, or bogging down your system. (You are thinking game mechanics terms again.) There can only be 3 asteroids active at one time, whether you put an expedition on them or not.

If you have researched Capture Asteroids, the game treats that 'roid as captured to Mars orbit from the time that your lander arrives at the asteroid. You will see the colors brighten on the lower right corner location switching display. You can make repeated trips to a captured asteroid. When you eventually Abandon it, it will just disappear, effectively blown out of orbit back into the Belt.

Well, that was super useful! Thanks for dispelling my worries.