Fast way:
Look for the index position of tag1 then look for the index position of /tag1. Then cut the string between those two indexes. Look up strpos and substr on php.net
Also this might not work if your string is too long.
$pos1 = strpos($bigString, '<tag1>');
$pos2 = strpos($bigString, '</tag1>');
$resultingString = substr($bigString, -$pos1, $pos2);
You might have to add and/or substract some units from $pos1 and $pos2 to get the $resultingString right.
(if you don't have comments with tag1 inside of them sigh)
The right way:
Look up html parsers