Here's the thing. Being felis domesticus of the well-fed, 21st century persuasion, my cat apparently views mice not as food, but as self-propelled playthings. So rather than delivering the death blow, she would periodically let the mouse go and then chase it again. This went on long enough to do several complete circuits of the office and dining room while I devised a gameplan to end the carnage.
My eventual plan involved putting on shoes (I had been lazing around barefoot), donning a pair of work gloves, and grabbing my trusty 5-gallon orange Home Depot bucket. I then joined the chase around the dining room. Eventually the cat cornered the mouse near the curtains, after several false starts, I manged to shake the mouse into the bucket from the bottom of the drapes where it had taken refuge. (The cat, not realizing what had happened, is still skulking around the drapes waiting for the mouse to re-emerge.)
The mouse seemed remarkably calm once it got into the bucket. I think it realized it had been given a reprieve from hours of torture by Goldie the Cat. I walked it to the vacant lot across the street and released it, hoping that maybe it won't feel like crossing the street to come back.