First, you need to know that this plant (and all other Euphorbias) has a very toxic sap that is a powerful skin and eye irritant. If it gets in your eye (e.g. brushing face with back of hand), it can cause temporary blindness. Be careful never to get sap in your eyes, or leave it on your skin. E. tirucalli has a particularly bad reputation for toxic sap, so be careful! Cut at branch nodes. Staunch the flow of sap with lukewarm water. Repot into an 8-inch container using Cactus and Succulent soil (or regular potting soil) mixed 1:1 with perlite, gravel, or pumice. The idea is to make a free-draining mix low in organics, but with more than 50% inorganic particles in the 1/8 to 3/8-inch range. This plant wants as much sun as you can give it. Growth will be much slower indoors. Allow the pot to completely dry before watering. Fertilize 3-4 times a year with any balanced fertilizer at 1/4 the normal strength. Happy growing!

Judging from the pencil cactus form, it need much more light to be happy. The segments are spindly from all the shade. Can you describe the soil? It needs to be a fast draining mix. Lots of perlite, or grit. It loo;s really black, rich and bad for a Euphorbia. Once you decide on a soil, one cuts off the rotted roots and let the cutting callus or get hard on the end. a week is a good time. then you stick it in the soil, and mist it. Do not water it. Mist it. At this time of year, your plant is probably going into dormance and it will not root till spring. One can pile some rocks around it to hold it up, but , with that height and thinness of the stem, one miight have to devise a means of propping. I have never rooted anything in the cold north so maybe one should wait to see if others from north of the sunbelt/Mason Dixie line has some pointers. I am still in the 90's and we are headed into a growth cycle. I imagine that rot is harder to avoid in your situation. I would make the soil very gritty. Pine bark, perlite, cjicken grit or Cactus soil and at least equal parts chunky perlite. Not the fine dusty stuff the big box stores sell.

Sorry, but I don't know or grow this plant (did so only very briefly), so I'll defer to other on this & Fred's suggestion sounds like a good start. But a caution, if you don't know, when you do cut it back (or for accidental breakage), best wear gloves or be extra careful to wash up & not touch your face 'til you do. If this is Euphorbia tirucalli, the white sap it exudes when cut can be a skin irritant. If its size is becoming an issue, there's no law that says you MUST repot it larger; you could keep it in the same size pot, & perhaps control its size SOMEWHAT by doing so.

The water requirements of any indoor cactus is determined the amount of sun light it gets,which you did not mention. Cactus receiving 5,000 foot candles, the measure of light, which is about 1 foot from a south facing window, should be watered every 3-4 weeks. Greater intervals with less light but at least once every 2 months. To adequately moisten/wet the soil in the pot, place the pot in a container with enough water to just cover the pot, allow time for the soil to absorb all the water it can hold, remove from the water and allow to drain. What is most important is the that the soil reach it's maximum water holding capacity.