Thank you for reaching out to ask2.extension.

According to what I have read, they should dry up naturally before cutting them back.  In order to bloom, amaryllis bulbs must be allowed to go dormant and exposed to cool temperatures for at least 8 to 10 weeks.

To induce dormancy, place the plant in cool, semi-dark location in late September and withhold water. Cut off the foliage when the leaves turn brown. Then place the dormant bulb in a 50 to 55°F location for at least 8 to 10 weeks. After the cool requirement has been met, start the growth cycle again by watering the bulb and placing it in a well-lit, 70 to 75°F. Keep the potting soil moist, but not wet, until growth appears.

The other option is to place the plant in a well-lit, 50 to 55°F location in fall. Maintain the amaryllis as a green plant from fall to mid-winter. After the cool requirement has been met, move the plant to a warmer (70 to 75°F) location.

I found this information on the Iowa State University Extension and Outreach.

I don’t grow amaryllis, so I wish you the best of luck!