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

The following is what you are looking for. Place it in your functions.php file making appropriate changes.

function custom_excerpt() {
    $text = get_the_excerpt(); //Assigns the excerpt to $text
    $text = str_replace("Word1_to_replace","", $text); // replacing the word with empty string
    $text = str_replace("Word2_to_replace","", $text);
    $text = str_replace("Word3_to_replace","", $text);
    return $text;
}
add_filter('the_excerpt', 'custom_excerpt');

Not really the most efficient way but this should work:

function the_excerpt1($s='')
{
    if($s !== '')
    {
        $a = explode(' ', $s);
        array_shift($a);
        array_shift($a);
        array_shift($a);
        $s = implode(' ', $a);
        unset($a);
    }

    return $s;
}

echo the_excerpt1('the content starts this is the excerpt');

Update - A more efficient way

function the_excerpt2($s='')
{
    if($s !== '')
    {
        $s = substr($s, (strpos($s, ' ')+1));
        $s = substr($s, (strpos($s, ' ')+1));
        $s = substr($s, (strpos($s, ' ')+1));
    }

    return $s;
}

echo the_excerpt2('the content starts this is the excerpt');

the_excerpt2() will execute 50-66% faster than the_excerpt1()

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.