In the .yml definition, I'm always pulling the latest image of my service.
When I push a new image to the registry and I want to update the image that the service in my stack uses. I don't see any --pull flag, and the documentation for docker service update doesn't explicitly mentions this.
How can I re-deploy using the recently pushed latest image?
You really shouldn't use latest in production or anything beyond local machine testing/learning. It makes everything ambiguous as to which image you're using, and you can't tell in docker service ls/ps if it's current by default and all sorts of other ambiguities (like SHA's not being visible in Docker Hub's GUI).
If you have no way around it, at least Swarm tries to query your registry and check for an updated SHA. If it sees one with docker service update --image <username>/<repo> <servicename> then it will pull and do a rolling update. You can watch docker events to be sure things are happening, and you can use docker service ps --no-trunc <servicename> to check afterward and see the SHA hashes of old and new images.