Is there any way to shorten the Livestamp.js time from '10 minutes ago' to '10m ago'?

It could be achieved by editing the defaultRelativeTime variable in the moment.js file from this:

var defaultRelativeTime = {
    future : 'in %s',
    past   : '%s ago',
    s  : 'a few seconds',
    m  : 'a minute',
    mm : '%d minutes',
    h  : 'an hour',
    hh : '%d hours',
    d  : 'a day',
    dd : '%d days',
    M  : 'a month',
    MM : '%d months',
    y  : 'a year',
    yy : '%d years'
};

To this:

 var defaultRelativeTime = {
        future : 'in %s',
        past   : '%s ago',
        s  : 'a few seconds',
        m  : '1m',
        mm : '%dm',
        h  : '1h',
        hh : '%dh',
        d  : '1D',
        dd : '%dD',
        M  : '1M',
        MM : '%dM',
        y  : '1Y',
        yy : '%dY'
    };

But is there any other way in which it could be done WITHOUT modifying the moment.js file?

You can customize the relative time format for your locale using updateLocale function. You need to pass the relative time object to it. In your case:

moment.updateLocale('en', {
relativeTime : {
    future : 'in %s',
    past   : '%s ago',
    s  : 'a few seconds',
    m  : '1m',
    mm : '%dm',
    h  : '1h',
    hh : '%dh',
    d  : '1D',
    dd : '%dD',
    M  : '1M',
    MM : '%dM',
    y  : '1Y',
    yy : '%dY'
}});