How to send email in wordpress with more than one attachments

Don’t know if that will solve all your problems, but:

Generally nicely formatted code is easier to debug. E.g. your code is missing the closing brace. Besides it is better to write if/else(if) statements with braces. Nice indentation helps too. I’d suggest reading the WordPress – PHP Coding Standards.

Regarding your code:

• As noted at the wp_mail() codex page the wp_mail_content_type filter should be removed after adding it to avoid problems.
• The file(s) of the $attachment parameter have to be given as path.

I’ve updated your code a bit:

if( isset( $_POST[ 'Save' ] ) ) {

    function my_custom_email_content_type( $content_type ) {
        return 'text/html';
    }

    if ( ! function_exists( 'wp_handle_upload' ) ) {
        require_once( ABSPATH . 'wp-admin/includes/file.php' );
    }

    $files = $_FILES[ 'my_files' ];
    $upload_overrides = array( 'test_form' => false );

    $attachments = array();

    foreach ( $files['name'] as $key => $value ) {
        if ( $files[ 'name' ][ $key ] ) {
            $file = array(
                'name'     => $files[ 'name' ][ $key ],
                'type'     => $files[ 'type' ][ $key ],
                'tmp_name' => $files[ 'tmp_name' ][ $key ],
                'error'    => $files[ 'error' ][ $key ],
                'size'     => $files[ 'size' ][ $key ]
            );
            $movefile = wp_handle_upload(
                $file,
                $upload_overrides
            );
            $attachments[] = $movefile[ 'file' ];
        }
    }

    $to        = '[email protected]';
    $subject="Contact Us";
    $message="Haiii";
    $headers[] = 'From: ' . get_option( 'blogname' ) . ' <[email protected]>';

    add_filter(
        'wp_mail_content_type',
        'my_custom_email_content_type'
    );
    $wp_mail_return = wp_mail(
        $to,
        $subject,
        $message,
        $headers,
        $attachments
    );
    if( $wp_mail_return ) {
        echo 'Mail send';
    } else {
        echo 'Failed';
    }
    remove_filter(
        'wp_mail_content_type',
        'my_custom_email_content_type'
    );
}