The Mutes of Arranger are an in-depended set of values to be applied on the Mute (more precise Quick Mute) of the entire project, therefore they apply in Arrangement Mode when the Arranger-Mutes are read which is at the beginning of each ROW. If you like to immediately Mute you will turn on QuickMute View and then opening the Arranger and maybe the Arranger-Edit, the QuickMutes are still visible and controlling the entire Project here unless you open Arranger Mute states of one of the Row, in which case those override the controlview but are still applied at the next Row-Entry.
That makes also technically sense because in a Live-Set you don’t want Mutes to apply in the middle of a beat therefore cutting it. QuickMute cuts the sound of a channel by User interaction, so on purpose. And because both “views” look same same on the Sequencer-Buttons, it can be quite confusing. Rule: QuickMute of the Project have higher priority than Arranger-Row-Mutes.
This limitation made me a couple of yours ago invest in a Faderfox PC12, never regret, ever since i Mute with Volume per Channel with a potentiometer just same as if i would Dj