Using "by mistake," how should the action of unintentionally deleting a file be expressed?

The phrase "by mistake" specifically emphasizes that the action of deleting the file was unintentional. The option that incorporates "by mistake" directly into the sentence—"I deleted the file by mistake"—properly conveys this meaning. It clearly states that the deletion was not deliberate and aligns with the requirement to use the specific expression provided in the question.

While other options may convey similar meanings, they do not utilize the exact structure needed. For instance, "I deleted the file mistakenly" and "I accidentally deleted the file" both imply unintended actions but do not include the phrase "by mistake." Additionally, "I have deleted the file by mistake," while grammatically correct and coherent, introduces the present perfect tense, which may not be as suitable for statements focusing on a specific past action. Therefore, the chosen answer effectively fulfills the requirement of using "by mistake" in a direct and straightforward manner.