The most efficient solution is the strtok function:
strtok($mystring, "https://stackoverflow.com/")
NOTE: In case of more than one character to split with the results may not meet your expectations e.g. strtok("somethingtosplit", "to") returns s because it is splitting by any single character from the second argument (in this case o is used).
@friek108 thanks for pointing that out in your comment.
For example:
$mystring = 'home/cat1/subcat2/';
$first = strtok($mystring, "https://stackoverflow.com/");
echo $first; // home
and
$mystring = 'home';
$first = strtok($mystring, "https://stackoverflow.com/");
echo $first; // home