The problem seems come from Virtuemart registration, I tried to switch to Protostar - a standard template of Joomla to test registration feature but it did not work either:
It means that the issue doesn't come from template.
Then I access this plugin: VM Framework Loader during Plugin Updates to disable Virtuemart registration redirection so it can use the default registration page of Joomla. But it looks like the email function on your site doesn't work.
You should contact your hosting provider for help to configure this email function.