Theres the explode function:
this will do it:
$date = "2002-02-27";
list($year,$month,$day) = explode("-",$data);
This will break it down by the - and then assign first the year, and so on.
Then put this through the script.
So what you want is:
list($year,$month,$day) = explode("-",$data);
$day=$day-14;
echo date ("Y-m-d" mktime(0,0,0,$month,$day,$year));
The best way for you to do your form, is to have 3 drop down boxes. One for month, date and year, so their put in the right order by the user. You will have to add the security to stop them having 31st Feb - as with mk time thats 3rd day in march. php.net link has an example of how to do this.