Old Ironsides is a nickname for a US Navy masted frigate that was named the USS Constitution by the first president of the country, George Washington. The poem was written in 1830, when the ship was to be decommissioned (i.e., taken out of active service). The poet, who may be the poem's speaker as well, seems to feel quite angry about the ship's fate. The speaker ultimately argues that it would be better for the much-honored ship to sink to the ocean's floor or to be set adrift during a storm than to bear the dishonor of being decommissioned. He even calls the people who want her decommissioned "harpies" in the second stanza. It is certainly ironic that the speaker and poet would call for the destruction of the ship rather than see it taken out of service; one would likely expect someone who respects the ship and its service so much to want it preserved for posterity. Certainly, the speaker uses verbal irony in the first line when he declares, "Ay, tear her tattered ensign down!" He does not want this at all, and he seems to taunt those who do.
In this sense, then, the tone is certainly ironic and even mocking of those individuals who want to decommission the ship. The poet presents the narrator as articulate, intelligent, and informed, and so it seems that we are to agree with him and see him as the poet's own mouthpiece. Therefore, we can ascertain that the poet feels as the speaker does: angry and indignant about the fate of this great ship.