Honestly that line "versus you a piece of ****" seemed to be more of a catch phrase to make him look good.
It could have been that Mundus was reassuring himself that he was still strong enough to take Dante on...or he really still could have thought that Dante was less than sh!t.
Besides, I would have thought his catchphrase was 'you don't **** with a god.' That seems more like a catchphrase to me.
I just don't think Mundus underestimated Dante. As for Vergil he didnt know he was a nephilim so he had no reasons to be worried there.
If Mundus truly underestimated Dante then he wouldnt be monitoring or being worried about him.
But maybe he didnt underestimated Dante nor overestimate him? I just dont think he underestimated him. For a god that is...
Due to Mundus thinking that he is like a god, I think his only concern about Dante would be that he was literally a 'loose end' as Mundus said.
A loose end is something left over, something that just has to be dealt with because it is there. In the case of Dante, he was what was left over from Sparda betraying Mundus.
And at the start of the game, Dante is a drunk, hungover bum, who is more interested in a good time. He doesn't have a clue about his parents, what he really is or where his life is going. The way Dante is at the beginning of the game, there's no chance of him finding out what he was, or wanting to get revenge for his parents. The Dante at the start of the game was not a threat to Mundus.
I'd say it was a matter of personal ego and pride for Mundus to kill Dante. To know Dante was dead would put his mind at ease and know that he was stronger than Sparda and his bloodline.
He constantly refers to Dante as 'the son of the traitor' or the spawn of Sparda, so that would indicate that the main reason he wants Dante dead is because he is a living symbol of Sparda's betrayl of Mundus. Killing Dante would ease the betrayl.
Even when Dante kills the succubus, Mundus is angry, but he's not freaking out or panicking. Then when Bob is killed, Mundus is still gloating in his tower, and at this point he is aware that Dante is affiliated in some way with The Order. He just doesn't take The Order or Dante as a serious threat because he's too confident that SWAT will wipe them all out in the raid.
Even when his heir is killed, he's still saying Dante is a 'piece of ****'. Then when they confront each other in his office, he doesn't attack right away. Instead, Mundus is calm and asking questions and debating what freedom is. If he thought Dante was a real threat, he would have attacked as soon as Dante got near him. Instead, it took Dante insulting him and gloating about the death of his child to get Mundus angry enough to attack.