docker-compose stop to stop the stack docker-compose start to start the stack
Both above will not remove your container, but rather shutdown and start them again, without any loses, even on the container filesystem, not only the volumes
docker-compose down will remove the containers of your services and all anonymous volumes assigned to them.
Be aware, not all changes in the docker-compose file can be applied using start/stop, rather most of the time, you have to do a down/up. Things like volumes/ports cannot be hot-applied like this.