Congrats on keeping your Mandevilla going for a few yrs! Not the easiest plant to keep alive over winter in a cold place.
Separating individuals potted together is not division, it is just separation. Without being able to see the root system your plant(s) has (have), one can only guess but they will either fall apart from each other if the soil is not compacted and holding everything together, or they could need to be sawed apart if they are compacted together. Depends on the soil type, whether or not it will just fall off of roots or if it is hopelessly stuck.
If I kept potting-up instead of repotting (remove old soil, trim roots), some of my plants would be in 50-gallon drums after having them for a few decades. If one has only potted-up plants, they would have no basis for comparison regarding repotting.
Plants in pots are no different from plants in the ground, which gardeners move/divide/prune as needed.
No plant likes to be rootbound. That means there is no more room for growth, and the amount of foliage that can be sustained stagnates. What is necessary for plants to stay alive is for their roots to not rot, which can happen so easily in a pot with dense soils, like ground dirt, or bagged mixes of predominantly tiny particles of peat, (or to simply shrivel from simply never getting any water.) Having very little soil around the roots would make the soil dry more quickly, and for even the most dedicated plant-overwaterers to not rot the roots of their plants. This is not ideal, since most non-cactus plants are stressed by dry conditions, it's just a way of coping with soil that has little air in it when moist.
Negative experiences in regard to potting-up, where an undisturbed root ball is placed into a bigger pot with more soil around it, vs. doing a repotting, as described below, can give rise to old wives' tales about plants not liking to be repotted/disturbed. Potting-up a root-bound plant that has roots surrounding the outside root ball often lead to this negative experience because those roots had adapted to accessing oxygen around the outside of the root ball and surrounding them with more dense, soggy-but-airless potting soil will likely lead to suffocation.
The reason bonsai masters are able to keep potted entities alive for hundreds of years is because they care for the roots by trimming them and changing the soil. A plant grows from the roots-up, so if the roots are not healthy, gorgeous foliage will decline &/or no flowers can form. When you unpot a plant and find a pancake of roots at the bottom, chopping that off will give roots a chance to grow normally again for a while and will make removing the old soil easier.
Roots need oxygen & moisture at the same time to function. Just air = shriveling. Just moisture = suffocation & rotting. Either will cause root death and dessicated foliage because the roots have been unable to deliver moisture. Having to let soil dry, as if ones' tropical jungle plant was a cactus, is an unnecessarily stressful coping mechanism for non-desert dwelling plants in soil without enough oxygen for the roots to stay healthy when it is moist and can lead to premature loss of older leaves and in extreme cases, dry shriveled roots/dead plant.
The ability of roots to be able to function properly depends greatly on the soil structure/texture, which can change over time. Potting soil tends to be very dense, mostly peat, with very little air in it. Any kind of organic ingredients decompose into smaller bits over time, and roots fill air spaces over time as they grow through soil. Replacing soil periodically is usually necessary to keep plants healthy because of these reasons. A more porous, chunky, airy soil (like cactus/palm, if one is buying bagged,) can have more air in it even when it is moist because there is space between the particles. When there are tiny particles of any kind in a pot, such as peat, sand, silt, clay, they filter into all of the tiny spaces in a pot, eliminating the air. "Overwatering" is the label and manifestation when roots have suffocated and/or rotted, combo of both. Over time, organic bits decompose into smaller bits, so even the "best" soil, if it has organic components, will need to be replaced when this happens. The speed at which this happens depends on many variables, but on average, about 1-3 years.
