Ignore means that you will not pay attention to something - you'll pretend that it doesn't exist.
(example) Your mother is asking you for the 100th time, when will you give her grandchildren?? You reply: "I don't hear you, I'm ignoring these questions!"
Deny means to protest or negate something.
(example) Someone accuses you of trespassing on their property. You reply, "I deny that accusation, I wasn't even in town on that day."
- For Teachers