I think it's a good question besides I'm curious so I made some research and found a workaround for this. It's a bit complex. I'm not sure worth it or not.
The first thing all, Postman Mock Server (in short Mock Server) cannot execute any test and pre-script so it is not capable to compute things. You need a calculation here so what are you gonna do? Well, you can define an environment
for Mock Server which gives you the ability to use dynamic values in mock responses.
I will continue step by step to show the process.
1 - Open a Mock Server with an environment:
1.1 - Create a collection for the new Mock Server:

Your mock response will look like below:
{"due_date": "{{date}}"}
1.2 - Create an environment:

1.3 - Finish to create:

1.4 - When you finish, Postman creates a collection like below:

1.5 - You can test your Mock Server from this collection:

As you can see, Mock Server uses the environment variable in their response.
Now, We have to figure out how to update the environment variable.
You have to use an external service to update your environment variable. You can use Postman Monitor for this job because it can execute tests (means any code) and works like a CRON job which means you can set a Postman Monitor to update a specific environment variable every 24 hours.
2 - Open a Postman Monitor to update your environment:
2.1 - This step is pretty straightforward, create a Postman Monitor like the below configuration:

2.2 - Write a test to update the environment:

The test will look like below:
// you have to use pm.test() otherwise Postman Monitor not execute the test
const moment = require("moment");
pm.test("update date", () => {
// set date 2 days past
let startdate = moment();
const dayCount = 2;
startdate = startdate.subtract(dayCount, "days");
startdate = startdate.format("YYYY-MM-DD");
// this is not work on Postman Monitor, use Postman API like below
//pm.environment.set('date', startdate);
const data = JSON.stringify({
environment: {
values: [
{
key: "date",
value: startdate,
},
],
},
});
const environmentID = "<your-environment-id>";
// Set environment variable with Postman API
const postRequest = {
url: `https://api.getpostman.com/environments/${environmentID}`,
method: "PUT",
header: {
"Content-Type": "application/json",
"X-API-Key":
"<your-postman-api-key>",
},
body: {
mode: "raw",
raw: data,
},
};
pm.sendRequest(postRequest, (error, response) => {
console.log(error ? error : response.json());
// force to fail test if any error occours
if (error) pm.expect(true).to.equal(false);
});
});
You cannot change an environment variable with pm.environment
when you using Postman Monitor. You should use Postman API with pm.sendRequest
in your test.
You need to get a Postman API key and you need to learn your environment id. You can learn the environment id from Postman API.
To learn your Environment ID, use this endpoint: https://www.postman.com/postman/workspace/postman-public-workspace/request/12959542-b7ace502-4a5a-4f1c-8164-158811bbf236
To learn how to get a Postman API key: https://learning.postman.com/docs/developer/intro-api/#generating-a-postman-api-key
2.3 - Run Postman Monitor manually to make sure tests are working:

2.4 - As you can see Postman Monitor execute the script:

2.5 - When I check the environment, I can see the result:

You can test from browser to see results:
