Kinetically.
Let the star run. It is a pain in the butt to shut down and anyway it is still really hot once you do. Also it is liable to restart while you are poking around in the guts. Plus if you shut it down it stops making stuff for you. That is like cutting down an apple tree to get at the apples.
Instead, kick chunks out of the center. Here is the scheme.
Identify sizable chunk of strong stuff that you don't need. A planitesimal will do.
Accelerate sizable chunk to speed.
Allow fast moving chunk to plow into star. It will lose material to ablation on the way in, which is why it is sizable.
Solid stuff hit in the center will be ejected out, according to Newtonian physics.
Have stuff positioned to catchCatch that stuff at some distance from the star. That is the good stuff you want.
If your chunk does not kick material out of your star, try a larger chunk and greater speed and maybe a different angle, hitting the core at the edge.
For a fiction this would be extra awesome because of the weaponization potential. The aliens would scoff at the futility of trying to hit them with a giant rock they can easily dodge. The rock is instead thrown at the star...