Saxon's hunt had led him to meet quite a few characters on the way to his objective. Most, if not all of them, have been violent encounters.
Saxon has a bitter hatred for "Hannah", holding a grudge against her for making him give up a human kill that was so easy in front of him. He never forgets a face, or a physical feature, and has sometimes went out of his way to find and attempt to kill Hannah to take her head as a trophy. None of these attempts have been a success.
Being the prey that was ripped from his grasp before he could have a chance, Takeo Misaki is one of Saxon's prime targets in order to keep himself from his own embarrassment. Saxon and Takeo have not interacted much outside of taunts from both parties, and fights interrupted abruptly by Hannah.
It's a funny thing between these two. While Saxon sees Aiden Misaki as a target, he doesn't see her as worthy enough prey to waste time with. This usually either leads to him just throwing her aside or ignoring her completely when there are other things to hunt.
Saxon sees Celtic less as an enemy and more as a worthy opponent to test his might against, and one he truly admires as a rival. He hopes that they'll never be able to kill one another in combat, to ensure their fighting lasts a lifetime. He's often even saved her life when she was outnumbered by Colonial Marines because, in his words, "You are only mine to kill".