Absolutely not.
He died once, rose from the dead, ascended into Heaven, and can never again be harmed in any way.
Rather, He graciously allows us who come along later to participate in His once-for-all sacrifice.
Under the appearances of bread and wine, we are permitted to consume the Lamb That Was Slain, just as the Israelites ate the sacrificed lamb in the Passover meal.
Likewise, we are permitted to join Him in making the one acceptable offering to the Father. Our earthly altars become one with the heavenly altar, and Jesus our High Priest acts through His earthly priest to let us experience and participate in that heavenly moment.
Just as Malachi the prophet revealed, in these latter days even the Gentile nations are enabled to make a pure offering to God – the one and only truly pure offering, namely the broken Body and shed Blood of His Son. And the Mass (including its Eastern counterparts, more properly termed the Divine Liturgy) is indeed offered “from the rising of the sun to its setting,” whether you take that to mean from East to West throughout the world, or at every moment of time.
Usagi