"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....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" (Session 22, chapter 2).
I did a web search to find the source for the quote you gave. Here is what I found:
CHAPTER II.
That the Sacrifice of the Mass is propitiatory both for the living and the dead.
And forasmuch as, in this divine sacrifice which is celebrated in the mass, that same Christ is contained and immolated in an unbloody manner, who once offered Himself in a bloody manner on the altar of the cross; the holy Synod teaches, that this sacrifice is truly propitiatory and that by means thereof this is effected, that we obtain mercy, and find grace in seasonable aid, if we draw nigh unto God, contrite and penitent, with a sincere heart and upright faith, with fear and reverence. For the Lord, appeased by the oblation thereof, and granting the grace and gift of penitence, forgives even heinous 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 indeed of which oblation, of that bloody one to wit, are received most plentifully through this unbloody one; so far is this (latter) from derogating in any way from that (former oblation). Wherefore, not only for the sins, punishments, satisfactions, and other necessities of the faithful who are living, but also for those who are departed in Christ, and who are not as yet fully purified, is it rightly offered, agreeably to a tradition of the apostles.
It is convoluted English. Quite detailed and difficult to decipher. It appears to say that there is one sacrifice that is bloody which would be the sacrifice on the cross and that there is another sacrifice that is not bloody which would be the sacrifice of the mass that occurs every time there is a mass. Then comes the complicated part which looks like it means that the bloody sacrifice is the same sacrifice that happens in the mass in every way except in the mass it is not bloody.
A little later in the 22 session there are some "canons" given which say:
ON THE SACRIFICE OF THE MASS
CANONS
CANON I.--If any one saith, that in the mass a true and proper sacrifice is not offered to God; or, that to be offered is nothing else but that Christ is given us to eat; let him be anathema.
CANON II.--If any one saith, that by those words, Do this for the commemoration of me (Luke 22:19), Christ did not institute the apostles priests; or, did not ordain that they, and other priests should offer His own body and blood; let him be anathema.
CANON III.--If any one saith, that the sacrifice of the mass is only a sacrifice of praise and of thanksgiving; or, that it is a bare commemoration of the sacrifice consummated on the cross, but not a propitiatory sacrifice; or, that it profits him only who receives; and that it ought not to be offered for the living and the dead for sins, pains, satisfactions, and other necessities; let him be anathema.
CANON IV.--If any one saith, that, by the sacrifice of the mass, a blasphemy is cast upon the most holy sacrifice of Christ consummated on the cross; or, that it is thereby derogated from; let him be anathema.
CANON V.--If any one saith, that it is an imposture to celebrate masses in honour of the saints, and for obtaining their intercession with God, as the Church intends; let him be anathema.
CANON VI.--If any one saith, that the canon of the mass contains errors, and is therefore to be abrogated; let him be anathema.
CANON VII.--If any one saith, that the ceremonies, vestments, and outward signs, which the Catholic Church makes use of in the celebration of masses, are incentives to impiety, rather than offices of piety; let him be anathema.
CANON VIII.--If any one saith, that masses, wherein the priest alone communicates sacramentally, are unlawful, and are, therefore, to be abrogated; let him be anathema.
CANON IX.--If any one saith, that the rite of the Roman Church, according to which a part of the canon and the words of consecration are pronounced in a low tone, is to be condemned; or, that the mass ought to be celebrated in the vulgar tongue only; or, that water ought not to be mixed with the wine that is to be offered in the chalice, for that it is contrary to the institution of Christ; let him be anathema.
You may have a point, it does looks like the teaching may be that Christ offers himself at every mass. Perhaps a Catholic can explain why that is either correct or incorrect.