How to remove first three words from content and display the excerpt

Here’s a quick way to do it, assuming $excerpt has your excerpt you want to remove the first 3 words from

$excerpt = "the content starts this is the excerpt";
$words = explode(' ', $excerpt);
array_shift($words); // 1st word
array_shift($words); // 2nd word
array_shift($words); // 3rd word
$excerpt = implode(' ', $words);

It splits the excerpt into an array of words based on the space ‘ ‘, shifts the first 3 words off the array and recombines it back into a string.