Exaltation of the Cross. Notion: as we try to understand things, we try to synthesize the many inside of the one, as the one is defined by the concept. So to answer the question of why the method of execution is venerated requires us to incorporate the process of execution into the thought, and in synthesizing this, we come up with the notion that this motion, this event, was the cause of the worthwhile thing. But the killing wasn't what caused the grace.
When we consider the concept, we have to say that although we use it as a referent, there are parts of it we don't understand, and that the event might not carry its significance as events are usually understood in the world. The fact of the event, yes. But If I think of someone going to to the well for water, and say that something happened because of that, the listener's Newtonian mind starts wondering what sorts of reactions and consequences might have been brought into the world by that physical action, but my statement might equally have referred to the fact of the event. The fact of having gone to the well for water had a result in the world. In the same manner, the fact of having been killed might be the cause of good, rather than thinking of it according to the mind of sacrifice, and concluding that the murderer provoked the grace.