When I hear the word “mystery,” I often think of the New Testament meaning of the word, as it frequently refers to a type of puzzle that–when properly discerned–can lead to a revelation. Paul in Ephesians 3 describes the Gospel as that type of mystery. Other times, especially in later church literature, a mystery is something inexplicable, that can never be fully understood. Both meanings may be present together.
When contemplating the mystery of Christ’s scourging, you can–as has already been suggested–focus on the source of Christ’s own suffering, whether it is the cruel form of the whip the Roman soldiers used, or whether it is your own sins for which he suffered and died. To be honest, though, this kind of meditative contemplation seems a little sadomasochistic, being very focused on the visceral suffering of Jesus, but failing to appreciate the significance of the event as “a mystery” unfurled over centuries, anticipated by the prophets, climaxing in the good news of the gospel.
You could also contemplate the prophetic Jewish material that described Christ’s suffering centuries before he was scourged. Contemplating the Old Testament material that the New Testament authors often referred to (by his stripes we are healed) is a great way to come to a deeper understanding of Christ’s suffering as understood and communicated by the evangelists. Engaging the biblical material in this way is an effective way to deepen not only your prayer life, but your appreciation for the message and mission of the apostles.
Further, you could contemplate your own personal sufferings as a Christian, or even just as a human being, in light of Christ’s scourging. While hopefully you’ve never been literally scourged for your profession of Christian faith, it is often productive to understand your own suffering in parallel with the voluntary suffering of Jesus. Perhaps this will help keep your frustration with nonbelievers in perspective, or lead you to commit more to Jesus/the Church/God in light of Christ’s voluntary suffering. Has God been calling you to offer something painful? You could think upon that.
When it comes to the Marian mysteries, I have a harder time, because I am not a mother; but when I do contemplate the mystery of her Assumption, I contemplate the things she had to endure–impregnated by the deity, reputation ruined, forced to flee her home, she watches her son tortured and executed by the state and then vanish into heaven; these are not the things parents normally long for. But her faith was rewarded.
Just some thoughts. I hope they help.