No is word that can be used to express different forms of the negative. In colloquial use the pronunciation can provide different meanings of "no" all within the same sentence; eg no, nuh, nah. Here "no woman no cry" literally translates to "stop woman don't cry".
She is already crying as seen in; "So dry your tears, I seh (say)". Bob is trying to cheer her up so invites her to reflect on how good it has been in the past; the good people, good times and good friends despite all of the hardships. Bob then shifts her focus on it being a necessary part of the struggle toward a great future. The cheering up is actually to prepare her for his leaving [again]. Bob repeatedly reassures her that everything is gonna be alright; so stop woman, don't cry.