no idea what it is,
persoanlly, i would cut it about a half inch above the joint between the 2 sections.

take the top 1/2, and cut it in half, discarding the bad piece, and try to root the top part.

you could make the first curt at the joint, but i am thinking the extra 1/2 inch may give it another place to start a new piece...

how much water has it been getting ?
what type of soil?

Greenman62,

Thank you for responding. I used Miracle Grow potting mix, but recently moved it the Miracle Grow garden mix. Not sure if there's a major difference. I water it throughly & let dry out between waterings. I read lots of warning on overwatering so I try to avoid it myself. Louisiana is nice, but got some cold front here & there the beginning of spring. Sometimes it got down to maybe 40s - 50s F. No frost though. Could that be the reason?

Pitayas like to be lightly watered every other day. It seems like the frost is causing the rot. You should cut that piece away from the main root to prevent future rotting.