You can get multicolor filaments but probably not "mixed" in the way you're imagining, like multicolor toothpaste as soon as you start using that, it would just mush into one combined color (and you probably could've just bought a nicer version of whatever color it combined into anyway).

Instead color is usually mixed along the length of the filament, gradually shifting color as layer after layer comes out, creating a multi-color gradient effect in the print. So-called "fast change" filaments change color quite quickly, transitioning to a new color as quickly as every few layers resulting in a "striped" appearance. "Slow change" filaments change more gradually, usually resulting in at most a two-tone or three-tone gradient except across very large/tall prints.

Filament changing for multi-color prints is also an option but requires either a complex and somewhat unwieldy filament unloading, switching and feeding apparatus or a tool-switcher or dual-extruders or other similarly advanced printer features.