You can do either. Their roots will be dead by spring anyway. I often cut them back in my pots, just to avoid having the soils scattered everywhere.

So they should pop back up in the spring? I don't need to reseed or replant or leave the remains in place? Sorry, real new at this.

Your portulaca has already reseeded itself. Those seeds will sprout in the spring. The 'mother' plant, which will die, can either be cut all the way back or plucked out and disposed of.

If there are any remaining seed capsules on your plant, filled with ripe, black seeds, you can collect them for spring sowing if you'd like.

collecting portulaca seeds is FUN!! After the bloom dies the center will dry up. when it is dry and brownish just carefully pop it off and you will find a bunch of seeds inside that look like poppy seeds. Make sure you have a little container handy.