In "Self-Reliance," what does "Out upon your guarded lips! Sew them up with packthread, do" mean?
The passage you give us here is sandwiched in between two of Emerson's more famous quotes from this essay. The meaning of those quotes closely matches the meaning of the passage you give. All of them basically mean that people should not worry about what others think about what they are saying. They should say what they think at all times.
The other quotes that surround your passage are
A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines.
Else if you would be a man speak what you think to-day in words as hard as cannon balls, and to-morrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day.
In these passages, Emerson is telling us not to worry about being consistent. He is telling us that we need to say what we think. In "your" passage, he is saying the same thing. He is saying that we should not "guard" our lips. We should not be worrying about what words pass our lips. If we're going to do that, we might as well just sew our lips up and not talk.
So, what your quote means is that we need to assert ourselves and say whatever we believe. We should not worry about others' opinions or about being consistent with what we've said before.