This is just an artistic representation of something that happened pretty early on in the comic, when John created a splinter timeline by listening to Terezi and skipping ahead to fight his denizen (resulting in his death, and them not being able to get Jade into the session). After four months, I think, Dave decides he needs to go far enough back in time to stop this from happening (and thus become Davesprite).
Before he goes, he has a conversation with Rose about what will happen to her when he leaves, whether she'll merge into her past self, continue to live on alone, or fade into nothing.
Saw this on the fora! Awesome as usual; it conveys Dave's determination to fix time and Rose's worry about what would happen to her. It looks as if the timetables are almost shredding her like a saw which is kinda macabre but fitting.