I don't know anything about mixpanel, but here are two ways to get the value of an input and store it in a variable for later use.
With jQuery (I prefer this method):
$('#mc-embedded-subscribe-form').on('submit', function(){
var val = $('input.email').val();
console.log(val); // Use this to test the function
});
Or with plain Javascript. First add this to the form
tag in your HTML:
onsubmit="getEmail()"
Then the JS function:
function getEmail() {
var elem = document.getElementById('mce-EMAIL');
var val = elem.value;
console.log(val); // For testing
}
Hope that helps :)