Final answer:
The simile used in the excerpt from 'An Occurrence at Owl Creek Bridge' is 'as an idler might observe the feat of a juggler, without interest in the outcome,' describing the protagonist's detached attention to his struggle.
Step-by-step explanation:
The phrase in the excerpt from "An Occurrence at Owl Creek Bridge" that uses a simile is "as an idler might observe the feat of a juggler, without interest in the outcome." A simile is a figure of speech that compares two different things using the words 'like' or 'as' to create a vivid image or connection in the reader's mind. In this case, the simile is used to describe the detached manner in which the protagonist is giving attention to his own struggle to free his hands, suggesting a lack of emotional investment in his predicament, much like an idle onlooker watching a juggler with no concern for the success of the performance.