What was Big Willy Shakes going for?
Thomas Mowbray is outraged when he is accused of treason. He uses the phrase "spotless reputation" after picking up on Richard II's line "Lions make leopards tame" right beforehand. He says that just as a leopard cannot change his spots, a man can't change his bad reputation.
It's as if men are like clay (read: easily molded). If someone taints their reputation, it carves that out of the clay. It's always there. You can't go back. He thinks it's completely unfair to accuse someone of something so awful. The accusation alone will ruin his good name.
And he's right. In Shakespeare's day, reputation was everything. There were no credit reports or background checks you could run on people. All anyone had to go on was someone's reputation. So it's no wonder it's a big deal in this play. An accusation of something, even if it turns out to be untrue, could ruin someone. So we totally feel for Mowbray in this scene.
But here's the thing: Mowbray's point might be right, but it doesn't really apply to him. Right after this scene, Shakespeare lets the audience in on a little secret: Mowbray did kill the king's Uncle Gloucester, but King Richard is the one who told him to do it.
Apparently everybody at court already knows this, but nobody's really doing anything about it. (Unless you count Bolingbroke, whose recent charge against Mowbray is obviously his passive-aggressive way of accusing the king of murder.) So while Shakespeare coined a new phrase with Mowbray, he was also being ironic. It turns out Mowbray doesn't have a spotless reputation after all.