According to the Divine Liturgy of St. John Chrysostom they do seem to offer the sacrifice for the Saints. Unless it really means to honor or is a translation thing. Here are some quotes from the DL...
"Again we offer you this spiritual sacrifice for those resting in the faith, the forefathers, fathers, Patriarchs, prophets, Apostles, preachers, evangelists, Martyrs, confessors, Aesthetics, and for every Holy Soul who has run the course in the faith. Especially for our all holy, spotless most highly blessed and glorious lady the theotokos and ever virgin Mary."
If I had to guess, I would say that they regard application of the merits of the Sacrifice differently than we do. First of all, and I am probably going to end up butchering this, they do not have a clear-cut distinction between mortal and venial sin, and --- here's where the possible butchering comes in --- they do regard prayers for the dead as being able to influence, or even
alter, the fate of the immortal soul. IOW, in Orthodox theology, it seems as though they don't regard the moment of death as a "done deal" WRT salvation or damnation. They do have the concept of "celestial toll houses", in which the newly-reposed soul runs a gauntlet of sorts, being judged as to various types of sins, with the angels pleading one's case, so to speak, and the soul being assisted by the prayers of the faithful (which I am assuming would include the Holy Sacrifice), while at the same time being accused by demons and having their sins "thrown in their face". Following this reasoning, and assuming that they see all of this happening outside of time, then there could (more butchering possible here) be spiritual advantage to offering prayers and sacrifice for saints who have already "run the gauntlet", in that they, too, went through the very same thing when they reposed, and they, too, were sinners.
There is a difficulty in applying this reasoning to Our Lady, as on the one hand they do not see Original Sin as we do, and thus the Immaculate Conception is something that is hard to fit into their theology, but on the other hand, they assert, as do we, that she was "all holy [and] spotless".
I'd be willing to bet, at this point, that the Orthodox would say something like "ah, Latins, there you go again, trying to explain a mystery that cannot be explained, that is beyond explanation or reason, just take the Divine Liturgy as it is and quit overthinking it". Or something like that.