document.getElementById("MyID").className =
document.getElementById("MyID").className.replace(/\bMyClass\b/,'');
where MyID is the ID of the element and MyClass is the name of the class you wish to remove.
UPDATE:
To support class names containing dash character, such as "My-Class", use
document.getElementById("MyID").className =
document.getElementById("MyID").className
.replace(new RegExp('(?:^|\\s)'+ 'My-Class' + '(?:\\s|$)'), ' ');