How fast can i stop taking 1mg of clonazepam if i have been taking it for 1year for anxiety?

Taper: I would taper it over a couple of weeks. Take 3/4 for 5 days, 1/2 for 5 days, 1/4 for 5 days and then stop. That will prevent any physical withdrawal. Of more concern would be recurrence of the underlying anxiety. Many antidepressants work well for anxiety (e.g. Paxil, (paroxetine) mirtazepine, and effexor).

Recommend tapering: Some people are very sensitive to stopping benzos, including klonopin (clonazepam). I generally recommend reducing it by 25% per week - if you have 0.5 mg tablets, start with 1 1/2 tablets for a week or so, then 1 tablet, then 1/2 tablet. If you get increasing anxiety, sweats, panic feeling, dizziness, nausea etc. Slow down the rate by which you taper. There are other meds which can help if you have trouble.