This isn't the article you asked for from the snippet you posted, but is about the same incident in that article. This article and others similar, appeared in dozens of papers across the country around April 24-25. Most all the other articles refer to her as just Miss Logan or give no name at all and say "a woman".
Apparently, from reading some of the other clippings, there was a group of individuals who were going around after the earthquake and stealing rings and jewelry off the dead bodies. They were cutting off the fingers of female victims to get the rings because their fingers had swollen, and they weren't able to just pull them off. It appears they thought Miss Logan was dead, when she was lying unconscious on the floor, and cut her finger off to get her rings.
San Francisco Chronicle
San Francisco, California
25 Apr 1906, Wed • Page 1
Clip:
https://www.newspapers.com/clip/113610493/san-francisco-chronicle/Do a search at Newspaper com for - "finger of her left hand", with Date of - Apr 1906
You will get over a hundred results from around the country & even Canada for Apr 25-26 about this incident.