May be a reference to two things:
1) The narrator’s life/nature continue to “grow” regardless of the fact that the narrator has suffered this tragedy.
2) The idea that the narrator is becoming (“growing”) “regardless.” That is, the narrator may be losing regard for their surroundings. This supports the first stanza, where the narrator is stiffening and growing cold due to the agony they are suffering.
To help improve the meaning of these lyrics, visit “After great pain a formal feeling comes (J341, F372)” by Emily Dickinson and leave a comment on the lyrics box