Place horseradish in the bowl of a food processor and pulse until finely chopped, stopping to scrape down the side of bowl as necessary.

Add vinegar and salt 1-2 minutes after horseradish is chopped for a mild horseradish, or 5 to 7 minutes for a hotter horseradish. Pulse to combine.

Immediately move horseradish to an airtight container and store in the refrigerator up to 4 weeks.