Since you specifically state that you are looking for a solution from the graph DB point of view, I will assume that what you are talking about specifically would be a Labelled Property Graph (LPG). (Investigating the Differences Between LPG, RDF and SPARQL)
That being said, the way that I would personally go about the described task, would be to not store the Tag information within the edge between the User and the Question. For reference, that would be the way you have described the schema in the question, namely being:
(User)-[SAVES {tags}]->(Question)
Solution
I would opt for a slightly more complicated schema, but would simplify the consumption of the data on your client side by quite a large degree.
(User)-[SAVES]->(Question)
(Question)-[TAGGED{users}]->(Tags{tags})
With this schema, you are essentially moving the tag information from the specific edge connecting a given User to a Question, and instead creating a new relationship from the Question to a Tags object, storing the given User as an edge property. This new object would just be a simple list of tags. Since the relationship is now defined from the Question as it's source you can walk the graph whenever someone adds tags to a specific question and merge any Tags with common User into a single edge.
Why have a {tags} Property on the Tags Node?
Adding the {tags} list property is simply a way to optimize the design for what I imagine would be a hot path in the scenario, and is not a required aspect of the given solution. The property would simply allow you to retrieve all of the Tag objects associated with a given collection of Users on the edge. If the {tags} property was omitted, it would be required to walk all of the edges from the Question to Tag nodes while keeping track of which users are on the edge in order to find that information.
(User)--[SAVES]-->(Question)<--[CLASSIFIES]--(Tag)
or some variant of that, maybe with a relationship between user and tag as well? Or somethng like(User)--[SAVES]-->(TaggedQuestion)
, which then in turn connects to the tags and the question itself?