Koi fish do exhibit predatory behavior towards other fish, which can be categorized into the following scenarios:

Dietary Factors
As omnivorous fish, koi will actively prey on small aquatic organisms like fry and shrimp when food is scarce. The dietary needs of adult koi may drive them to nip at or even swallow smaller conspecifics or other fish species.
Records of Special Cases
There have been observed extreme cases where giant koi instantly swallow other conspecifics. Such behavior is usually related to hunger or significant size differences.
Considerations for Mixed Breeding
Avoid keeping them with small tropical fish to prevent accidental ingestion.
Male koi become more aggressive during the breeding season and may nip at other fish.
When the stocking density is too high or water quality deteriorates, conspecifics may also bite each other.
For a more intuitive understanding of koi's predatory behavior, you can watch relevant video recordings. It is advisable to ensure an adequate food supply during rearing and choose fish of similar size for mixed breeding.