Another interpretation: "the blood upon the altar" - even though the flesh is no longer present [the blood still atones]. How then do I uphold the verse "And you shall offer your burnt offerings, the flesh and the blood" (Deuteronomy 12:27)? It compares flesh to blood: just as the blood is offered by dashing, so too the flesh is brought by throwing. One might think he throws it [and leaves it as it lands]; Scripture teaches, saying "and the priest shall arrange" - how so? He throws it and then arranges it upon the altar all around. This applies when the altar is whole all around, and not when a horn of the altar has been removed. Thus, if a horn of the altar was removed and one performed the service upon it, that service is invalid.
Blood Atones Even When the Flesh Is Gone
Yalkut Shimoni on Torah 441:3
דָּבָר אַחֵר הַדָּם עַל הַמִּזְבֵּחַ, אַף עַל פִּי שֶׁאֵין הַבָּשָׂר, הָא מָה אֲנִי מְקַיֵּם (דברים יב, כז) "וְעָשִׂיתָ עֹלֹתֶיךָ הַבָּשָׂר וְהַדָּם" מַקִּישׁ בָּשָׂר לְדָם, מַה הַדָּם בִּזְרִיקָה, אַף הַבָּשָׂר בִּזְרִיקָה יָכוֹל יְהֵא זוֹרֵק (וְעוֹרֵךְ) [וְרוֹבֵג] תַּלְמוּד לוֹמַר "וְעָרַךְ הַכֹּהֵן" הָא כֵּיצַד זוֹרֵק וְעוֹרֵךְ עַל הַמִּזְבֵּחַ סָבִיב, בִּזְמַן שֶׁהוּא סָבִיב וְלֹא בִּזְמַן שֶׁנִּטְּלָה קַרְנוֹ שֶׁל מִזְבֵּחַ הָא אִם נִטְּלָה קַרְנוֹ שֶׁל מִזְבֵּחַ וְעָבַד עָלָיו עֲבוֹדָתוֹ פְּסוּלָה.