Those needles used in acupuncture are reused?

or acupuncturists buy them?

It depends on where you live what the laws and rules for sterilization of acupuncture and other medical devices are.

In most of the US, state law requires acupuncture needles to be sterile, single-use disposables, used once and then disposed of as medical waste.

I concur with Jeannette. Most acupuncturists in the United States use pre-sterilized, one-time use needles.

Autoclaving (re-sterilizing) such thin instruments like acupuncture needles is often difficult and it has been reported to weaken the shaft of the needle.

Jonny L is mistaken in his assessment. Acupuncture needles often penetrate the dermis into the muscle layer. Bleeding can potentially occur even when the skin layer is not fully penetrated.

Finally, even if the did not penetrate the skin layer the second the needle comes into contact with the skin it is no longer sterile. This is true of any sterile device.

I believe they are reused but cleaned. In a reputable place they will have them cleaned. While this may sound unhygienic the acupuncturist does not use the needle to puncture the skin. The needle does not fully penetrate the dermal layer of skin but actually only goes in far enough so that the skin can hold onto it. If you will notice, you're not supposed to bleed when having it done properly. The purpose of this is to control the flow of chi and redirect it to areas where needed.