Add this line of code const mockedAxios = axios as jest.Mocked<typeof axios>. And then use the mockedAxios to call the mockReturnValueOnce.
With your code, should be done like this:
import myModuleThatCallsAxios from '../myModule';
import axios from 'axios';
jest.mock('axios');
const mockedAxios = axios as jest.Mocked<typeof axios>;
it('Calls the GET method as expected', async () => {
const expectedResult: string = 'result';
mockedAxios.get.mockReturnValueOnce({ data: expectedResult });
const result = await myModuleThatCallsAxios.makeGetRequest();
expect(mockedAxios.get).toHaveBeenCalled();
expect(result).toBe(expectedResult);
});