There are several rot problems associated with cacti and most are related to over-watering or using a planting medium that is too water retentive. If your cactus is showing soft brown patches on its fleshy segments (stem rot disease) first review the care you have been giving your cactus. For a quick review of proper cactus care, refer to our guide Cacti Indoors. Cacti receiving proper care rarely develop this disease. So begin your remedy by making any necessary adjustments to your cultivation routine. You can cut out the infected tissue.  

Rot at the point that the cactus emerges from the growing medium (basal rot disease), is a result of over-watering in winter. It is very important to differentiate the non-active growth period of your cacti and to give them a rest. From October through February, most desert cacti need reduced water, food and temperature, though direct sunlight should continue.

If you see rot at the tips of your cactus segments with shriveled flesh, again you have been over-watering in winter. Follow the advice for basal rot above.

Finally, if you suspect that you have over-watered to the point of rotting the very shallow and delicate roots of your cactus, or you have been using a moisture retaining soil that stays too wet, there is no choice but to remove it from its pot and inspect the roots.  If they are brown and mushy, your cactus will not survive.  If they are mostly still firm and healthy looking, trim away any mushy roots and leave the cactus out of its pot to dry out for several days.  Then replant it in fresh, proper, cactus planting medium and in a pot with a drainage hole.  Adjust your watering routine to avoid recreating the problem.

Courtesy of NYBG Plant Information Service