Q: How do I disprove the Defense's witness's claim?

A: Mock trial games are always made to seem hard at first but the possibilities really open up once you dig in. Since you are trying to disprove the defense witness's claim I'll assume you are the prosecutor.

The way I see it, the Waiter is the biggest problem for the prosecution. The Defendant has motive to lie to save himself. The Wife has motive to lie to save her husband. Unless there is an obvious lie in the materials for these two then no use keeping them on the stand any longer than absolutely necessary as that will only help the defense. Try to know the defendant's mock-trial material better than the actor playing the defendant or his wife. Catch them in "lies" that are really just mistakes where they mis-remember or misinterpret the mock-trial material. This will cost them credibility in the eyes of the jury.

The defense will surely say that the Teacher and Student are the real suspects since they are the only ones who have admitted to being at the scene of the crime AT THE TIME of the crime. So they would obviously throw the Defendant under the bus to save themselves. The Defendant and Officer may have been at the scene, but it was after the crime had happened.

You need to show why the waiter is lying or simply wrong. What possible motive is there for the Waiter to lie? The waiter has nothing on the line in this scenario. Re-read the material and look for anything at all that could give the waiter a motive to either be dishonest… or anything that shows the Waiter might be mistaken. Does the waiter have a memory problem? Exhausted from working long hours? Easily confused? Intoxicated from sampling the table wine? Maybe the waiter has some reason to personally care about the Defendant's welfare?

You mentioned a gun. Anticipate defense questions about the ACTUAL time of the crime. Just because someone heard A GUNSHOT doesn't mean it was THE GUNSHOT related to the incident. Also, pay attention to the supposed date of the incident. The weekend of the Daylight-Saving Time switch is over-represented in mock trial games and may be exploited by the defense.

Your strongest asset will be that the potential jurors are likely to make the mistake of trusting a Police Officer and a Teacher more than a Waiter. Use your questions to build up the apparent credibility of your Officer. Before asking about the investigation, introduce the Officer to the jury in a positive light by asking initial questions about years of experience and anything else positive your judge will let you get away with… it should be supported by the mock-trial background materials.

The more the Officer and the Teacher talk, the better your chances… assuming the students assigned to those roles do a good job. In the question as posted, the Student and Teacher basically have the same information so I will assume this is true. Jurors in real life would have more trust in the Teacher but the jurors in mock trial may be your fellow students… so your choice to focus on the Student or the Teacher may be basically whichever is the better student, the better prepared for mock trial, and/or simply more popular with peers. Finally, be prepared for the possibility that the Defense will suggest an improper relationship between the Student and Teacher. This would give them another reason to lie about what they saw and when.