His personality is a mix of the two zanpakuto spirits. As far as his personality goes, Saigetsu is serene and straight forward. His actions speak for themselves and he speaks only when he feels it is necessary. Most of the time, he is the voice of reason. He is also a strong, capable and formidable combatant, not to be taken lightly. Zangetsu is portrayed as calm, level-headed, and at times emotional. He often acts as a mentor to those around him and will always try to push those who he deems worthy enough to become stronger. Although Saigetsu is the merger of the two previous spirits, it seems that Tensa Zangetsu is for most of the time the dominate personality, though he is prone to occasional outbursts like the Hollow once had. After dying as a result of his previous master losing his spiritual powers and being reincarnated again as a whole new zanpakuto, Saigetsu has since then been looking for someone worthy enough to wield him once more, any potential opponent or candidate he sees, he will challenge them to a battle, to find out which one of them is stronger, as in the case of Takashi Kosuda.
Unless the individual has the right resolve and a strong heart Saigetsu won’t challenge them, and will leave them be. He will only challenge those who he deems worthy and will only fight against an opponent if threatened or provoked. Zangetsu is also shown to be very intelligent, he has great understanding of the world around him, as shown by his outstanding knowledge of the soul society and its working , he also seems to have a better understanding of zanpakuto’s and the relationship they have with their masters. Because of his calm and level-headed disposition, he is shown to be very serious for most of the time, rarely exhibiting humor. When he does so, his humor is very dry.
When he was a part of Ichigo Kurosaki and lived within his inner world, which was a world of tall glassy skyscrapers, Zangetsu claimed to prefer lusher, natural surroundings, like bright, sunny skies, green forests and animals. Oddly the Inner Hollow professes to demand the same things as well. When Muramasa once freed him of Ichigo's control, his reason for turning on Ichigo was very unique compared to the other rogue Zanpakutō spirits; while their reasons were all self serving, Zangetsu did not wish to leave Ichigo; he merely wished to see Ichigo achieve his true potential and find out who is the stronger of the two. This aspect of his personality seems to have remained, even till to this day. As a result of his reincarnation as a new Zanpakuto spirit Saigetsu has been given the chance of experiencing things that his original counterpart couldn't, as such he seems to enjoy life in his own way, appreciating the beauty of the outside world.
Although for most of the time he is seen as a calm and rational individual, he can also be very dangerous and manipulative. Some aspects of the hollow’s personality can be seen within him, as when this personality emerges he is very energetic, talks a lot, and is a sadistic, fierce fighter. He can also be very violent and impulsive. He will laugh maniacally and enjoys causing his opponents pain. He battles like a berserker, ignoring any sustained injuries or pain and mercilessly overwhelming his enemies with brute strength, sheer power and blinding speed. Hollow Ichigo's cockiness and impulsiveness shows in Saigetsu's personality, but it is overshadowed by Tensa Zagetsu’s strategic mind and concern for others (he ultimately used his violent and impulsive attitude to fool an opponent into thinking that he was nothing more than a lunatic, which gave him the chance he needed to finished the opponent off once and for all). Being a whole new being, he refers to his original counterparts as separate people as they would address each other. From bleachfanfiction
