I understand that mock = fake, and that to put sb through sth = to make sb experience sth. I agree with "put sb through a mock execution", because execution is an activity. But I don't understand how one could be "put through a mock firing squad", since a (mock) firing squad is a group of people. How does one experience a group of people?
You don't just experience the group of people. What you experience is whatever it is that that group of people has been put together to do.
For example, I used to work for the Civil Service. If you wanted to apply for promotion, you had to submit a paper application and then, if that was successful, you were invited to be interviewed by three senior civil servants. Those people, collectively, were referred to as "the interview board" or "the board". It was a fairly challenging, if not terrifying, interview and a lot of people were very nervous about the prospect. Consequently, some members of staff who had experience in these matters used to offer a service to people who were going to face the interview board - they would offer to do a "mock interview board" for them. It was basically a fake interview so that the person could practice what they might say and get used to the feeling of facing three people questioning them.
The person applying for promotion would say, for example "I've got my real board on June 27th. I'm not looking forward to it, but some of my colleagues have offered to help me in advance. On June 24th, I'm going to
go through a mock board."
We use the nouns "the firing squad" or "the board" not just to mean the group of people but to refer to the entire experience that they represent which, in both those cases, is something not at all pleasant!