Hi, thanks for posting an interesting project.
As I understood you wan't to deploy Vuejs application production mode to digitalocean hosting.
For that, we need:
1) Take a fresh ubuntu droplet on digitalocean.
2) Install and configure Node, mysql, and vuejs.
3) Upload your application files to GIT, I think you already have it.
4) Then we can simply change database and config variables in application and if everything is written with good practices then we can easily run vuejs application, we can make so that domain will listen to some port.
5) Installing SSL with letsencrypt is an easy task and can be done in about 30 mins.
I'm an experienced web developer working on fast, scalable, maintainable and fully automated websites and API-s for over 5 years and I think I can help you out with the project.
Please send a message and let's discuss further.
Thanks.
George.