What is the term for cutting into something with a sharp instrument?

The term referring to cutting into something with a sharp instrument is "incise." This word is derived from Latin, where "incidere" means to cut into or cut through. In various contexts, particularly in medical and artistic fields, "incise" is used to describe making precise cuts or incisions, which can be crucial for procedures such as surgery or when creating detailed designs.

In contrast, the other options do not convey the same meaning. "Incorporate" means to include or integrate something as part of a whole. "Inject" refers to forcing a substance into something, typically using a syringe, and does not imply cutting. "Imitate" means to mimic or replicate something, which is unrelated to the act of cutting. Thus, "incise" accurately captures the action of cutting into something with a sharp instrument, making it the correct choice in this context.