I think we are speaking of the term mystery in more than one way. The Greek and Latin terms give us the words "sacrament" and "mystery", by which we refer, more or less, to the making of something holy, set apart. John Chrysostom connects the idea that they are called mysteries because what we see is not what we believe. We see a man and a woman having sex, we believe in love. We see a bath, we believe the Church claims a soul as its own. We see a baby's cut foreskin, we believe the child is now part of his nation.
We see a man tortured to death on a cross, we believe something else. Perhaps.
Suffering can be seen this way: as a mysterious, sanctifying grace. Which is not to say we want it or that it is something good. On the contrary, suffering is entirely evil. But it does set us apart, it makes us different. Or, we could say that it doesn't make us different from lower animals, in which case the suffering of a man is no different from the suffering of a fish. This is what we mean by the term mystery.
I was there as my grandfather took his last breaths, in pain, unable to care for himself, barely conscious. And cold, during those last hours. There's no good that comes from it, it doesn't make me less sinful or bring glory to God or any of that nonsense. But it was a mysterious grace, this being with him as he suffered. It was set apart, special, in a horrible way. Fortunately, it is a grace I will never experience again: there was nothing good about it.
But it was a mystery. What we see is a primate in pain, what we believe is something else. Or not. This is what I'm trying to say to you.