Answer :
The participial phrase "struggling to its feet" describes the deer in that sentence :)
The answer to your question would be that the participial phrase modifies the word "deer". A participial phrase begins with a present or past participle and includes objects and modifiers that complete the thought.
Participial phrases always function as participles since they add description to the sentence. In this case, the participial phrase refers to "the newboorn deer".
