First, it's important to understand who the "We" are that Dunbar refers to in the poem. "We" refers to African-Americans specifically, but could apply to anyone or any group that is or feels subjugated. The mask symbolizes that which hides true feelings. The lines you cite are from the first stanza of this poem which says that people hide behind an acceptance of mediocrity. Dunbar says that rather than strive for perfection, many are content to let difficulties get in the way and then use those difficulties as an excuse for not succeeding or for being down-trodden. Dunbar feels that as an African-American, society expects him to accept this mediocrity that he is talking about and expects him to be content with it. He, however, is expressing his frustration and saying that people fight this tendancy and expecation.
This poem points specifically to the hardships and suffering of slaves. They were placed in such harsh conditions, and yet they did not show the pain. They did not wear their emotions on their sleeves. The made every effort to appear happy and content, while underneath the facade, they were emotionally torn up and beaten down. These lines emphasize the theme throughout the poem.
"With torn and bleeding hearts we smile" translates to just that. Although they hurt on the inside for all of the injustice of slavery and their conditions, they continue to smile. They show strength and endurance by doing this.
"And mouth with myriad subtleties" translates to their smiles having many different fine distinctions. In other words, their smiles held so many different meanings than just the simple happiness that they presented. So many other emotions were going on behind "their masks."