Often implies that the division is not equal or just among the involved parties. They carved up the business profits, leaving the smallest share for the youngest.
Pro Tip 2/3
Negative sense
Usually suggests a negative connotation, especially when used in personal or political contexts. The empire was carved up by greedy generals with no concern for the people.
Pro Tip 3/3
Metaphorical use
Can be used metaphorically to describe dividing intangible things, like time or attention. She carved up her day between work, study, and family.