After consulting the military board, Qutuz, May Allaah have mercy upon him, decided to chop off the heads of the four envoys sent by Hulagu, and hung them on Baab Zuwaylah in Cairo, in order to be seen by as many people as possible. By doing so, he intended to reassure the people about the fact that their leader does not fear the Tatars. This, without doubt, would raise their spirits.

At the same time, this violent reply would give the Tatars the impression that they would come to a people quite different from those whom they had already met, perchance it would leave a negative effect on them, and cast some terror and reluctance into their hearts. However, the greatest aim of killing the four envoys was to cancel out any deliberation about peaceful solutions, and completely and seriously get ready for Jihaad.

That is because after killing the four envoys, the Tatars would not accept the surrender of the Egyptians, even if the Muslims themselves accepted it.

That was the personal reasoning of Qutuz, May Allaah have mercy upon him, and the emirs.
Now, let us pause to reflect on that incident.

https://www.islamstory.com/en/artical/20789/what-did-qutuz-decide-to-do