Paula Angel was born around 1842 in Las Vegas, New Mexico Territory, into a prominent family. Details about her early life are sparse, but by her late teens, she became involved in a romantic relationship with Miguel Martin, a married man and father of five, who also hailed from a notable family in the area.

In March 1861, Miguel Martin decided to end his affair with Paula Angel, intending to return his full attention to his family. Distraught and feeling betrayed, Paula arranged a final meeting with Miguel. During this encounter, overcome by emotion and anger, she stabbed him in the back with a knife concealed beneath her shawl, leading to his death.

Paula was promptly arrested and charged with first-degree murder. The trial was swift; the presiding judge instructed the jury to consider only the charge of first-degree murder, excluding lesser charges such as manslaughter. Despite Paula's plea that the act was a crime of passion without premeditation, the jury found her guilty. She was sentenced to death by hanging, the mandatory punishment for such a conviction at the time. ​

On April 26, 1861, Paula was led to a cottonwood tree in Las Vegas for her execution, as no formal gallows were available. Her hands were left unbound, allowing her to grasp the noose in a desperate attempt to save herself. The attending crowd intervened, cutting her down and expressing their disapproval of the execution. However, the sheriff insisted on carrying out the sentence. After restraining her more securely, Paula was hanged a second time, this time resulting in her death.

Paula Angel's execution was largely overshadowed by the events of the American Civil War and received minimal contemporary attention. She remains the only woman to have been legally executed in New Mexico since its incorporation into the United States. ​