Back-up doesn't work in Craft CMS 3 on MAMP locally
I have just run into a similar problem.

I'm not sure if this is what fixed it but try creating an Envvars file as per jonlivingstone's comment here https://github.com/craftcms/cms/issues/2364

Once I had done that my backup ran. I then had to switch MAMP out of FastCGI mode otherwise I got a 500 error at the end of the update process.