You assigned a major project and are halfway through when you realize that you’ve made a mistake that require you go back to the beginning to fix.?

In  my approach, 

When I have been found a major mistake in the halfway of a project which was happened because of me means, the first thing I would stop all my activities whatever I am doing on the project and then I will investigate, analyze the impact of the mistake. If it is a small mistake enough that I can correct it by using PM’s schedule reserve analysis without losing time. Once rectified the situation immediately I move forward.

When it makes a major impact on the project timeline and deliverable need to think about the alternative solutions or else immediately I would inform my supervisors / team managers and let them know what is going on. It would be the situation then I could adjust my work accordingly. If needed I have to put additional time effort to make the deadline without compromising the reset of the project. If the mistake is a result of my project it’s a painful for me and I have to come clean. If nothing else, the learned things will be documented and it will be taken as an opportunity for any other peoples who are in similar situations and it helps them to come out from the major impediments in the project or dealing with similar scenarios. 

Did you try Agile techniques?

What if the entire project depends on this mistake?! I think it is better to come late than to come with a wrong project-life decicion. You can be forgiven to come late but right, but if you did something really bad, you may not be forgive.

I believe the best choice you have now is to start working again and fix the problem!