What does “proclaim Your death” mean, exactly? It sounds almost celebratory. Does it truly mean, “we remember Your death?” If so, ought not it be more clear - we “commemorate” or the priest re-enacts the death?
 
This recitation has only recently begun to disturb me, as I attempt to ponder seriously everything the members of the congregation recite.

You ask about the meaning of one of the responses to the invitation “Let us proclaim the Mystery of Faith” which occurs right after the consecration.  To the invitation Mysterium fidei (Latin) comes this response in Latin: Quotiescumque manducamus panem hunc et calicem bibimus, mortem tuam annuntiamus. Domine, donec venias, rendered in English as "When we eat this bread and drink this cup, we proclaim your death, Lord Jesus, until you come in glory."  (It is anticipated that a new translation will take effect in late 2011: “When we eat this Bread and drink this Cup we proclaim your death, O Lord, until you come again.”)
 
“We proclaim your death” could also be translated as: we announce your death, or we tell everyone about your death, or we advertise your bloody death on the cross carried out for our redemption, or the like.  The point of this acclamation is to activate us as witnesses and apostles to tell the whole world about the life of Jesus Christ, about His death and resurrection, about his everlasting mercy and goodness, and about “the reasons for hope within us” as St. Peter reminds us (cf. 1 Peter 3:15).
 
As Christians and disciples of Christ we do not “celebrate” his death in the sense of happiness and parties;  what we celebrate and rejoice about is his miraculous resurrection and victory over death which constitutes the most important proof of his divinity.  We proclaim his death because we should never forget what he has done for us. For that reason, the crucifix with the crucified body of Jesus Christ is displayed clearly in the sanctuaries of our Churches.

It is praiseworthy that you are pondering the deeper meaning of these words.  Keep digging! There are endless treasures for you in the robust yet austere liturgy of the Roman Catholic Church.  For more information about the new translations of the Roman Missal, be sure to check out the USCCB website at www.nccbuscc.org/romanmissal