Here is what the Council of Trent says regarding the “unbloody” nature of the Holy Sacrifice of the Mass (
Session XXII, Chapter 2):
And inasmuch as
in this divine sacrifice which is celebrated in the mass is contained and immolated in an unbloody manner the same Christ who once offered Himself in a bloody manner on the altar of the cross, the holy council teaches that this is truly propitiatory and has this effect, that if we, contrite and penitent, with sincere heart and upright faith, with fear and reverence, draw nigh to God,
we obtain mercy and find grace in seasonable aid. For, appeased by this sacrifice, the Lord grants the grace and gift of penitence and pardons even the gravest crimes and sins.
For the victim is one and the same, the same now offering by the ministry of priests who then offered Himself on the cross, the manner alone of offering being different. The fruits of that bloody sacrifice, it is well understood, are received most abundantly through this unbloody one…
From Trent, then, we see that the Church teaches that Christ is still the
victim (“the victim is one and the same”), Christ is still the
priest (“the same now offering by the ministry of priests who then offered Himself on the cross”), but Christ offers this sacrifice without again being slain and shedding his blood (since that has happened once and for all, and Christ no longer dies).
I don’t know that the Church officially teaches that we are “at the foot of the Cross”; rather, she teaches that the
sacrifice is “made present”.
Perhaps this means by extension that the circumstances or environment of the sacrifice (i.e. Calvary) are made present.