The simplest and most reliable way to reformat a date string is to just reformat the string. So use split (or match) to get the values and return them in the order you want, ignoring the bits you don't need, e.g.:
function isoToDMY(s) {
var b = s.split(/\D/);
return b[2] + '/' + b[1] + '/' + b[0];
}
document.write(isoToDMY('2015-11-09T10:46:15.097Z'));
If you want the output date to also consider the host system time zone (e.g. 2015-11-09T20:46:15Z in a timezone that is UTC+0530 will be 2015-11-10T02:16:15Z)), then you should manually parse it to a Date object and then get year, month and day values.
A library can help with parsing, but a function to parse and validate the values is only a few lines.