According to Catholic doctrine, how can an angel be a saint? In Catholic doctrine, a saint has to (a) be “a dead person” and (b) be “in Heaven”.


  How is someone deemed a saint? The pope canonizes a dead person who has lived a life of heroic virtue and has performed a posthumous miracle in addition to the miracle required for beatification.
  Peter Turner
  
  Being in Heaven is the definition of a ‘capital-S’ Saint.
  Ethel Evans


Alternatively, a saint may be an angel, though this is a different “category” of saint.


  Angels, like Saint Michael, may be called Saints but aren’t in quite the same category as human believers.
  James T.


So, what is an angelic saint? Are all angels saints, or just some of them? How is this determined?

I can see one possible solution: All angels are in Heaven, and are therefore saints (per Ethel Evans), but they are not ‘deemed’ as saints (or, not canonized), because (per Peter Turner) they are not dead. They are therefore a different ‘category’ of saint (per James T.). This makes sense to me, but is it valid?
By canonizing some of the faithful, i.e., by solemnly proclaiming that they practiced heroic virtue and lived in fidelity to God's grace, the Church recognizes the power of the Spirit of holiness within her and sustains the hope of believers by proposing the saints to them as models and intercessors.
CCC 828

Some angels have been recognized as saints because of their heroic virtue and fidelity to God's grace, and these angels can also fulfill the role of model and intercessor. One particular example is Saint Michael the Archangel, whom we know about from the book of Revelation.
Not all angels are saints because not all angels have heroic virtue and fidelity to God's grace. (Fallen angels are an example of this.) Also, while many angels are in heaven, there are few angels who are saints because we do not know enough about them to canonize them. Saint Michael is one of the few angels that we do know a lot about.
Also note that while we believe all saints are in heaven, simply being in heaven does not mean that a person is recognized as a saint.