How to redirect to a page after the form is submitted

You can remove the else statement so that user will see the message and will be able to upload csv again or you can redirect using

echo '<script>windows.location.href="' . $url . '"</script>';
die;

Edit

$admin_services = add_menu_page( 'Fee Schedule', 'Fee Schedule', 'administrator', 'pd-  services', 'pd_services' );
function pd_services() {
?>
<div class="wrap">
    <form name="csvupload" action="" method="POST" enctype="multipart/form-data">
        <table class="form-table">
            <tr>
                <th><label for="uploadcsv">Upload Services from CSV</label></th>
                <td><input type="file" name="service_upload_csv" id="upload_csv_id" aria-required="true"></td>
            </tr>
            <td>
                <p class="submit">
                    <input type="submit" class="button-primary" name="admin_service_csv_upload"
                           value="<?php _e( 'Save Changes' ) ?>"/>
                </p>
            </td>
        </table>
    </form>
    <?php echo $content ?>
</div>

function process_pd_services_upload() {
if ( $_SERVER["REQUEST_METHOD"] == "POST" && isset( $_POST['admin_service_csv_upload'] ) ) {
    if ( get_file_extension( $_FILES["service_upload_csv"]["name"] ) != 'csv' ) {
        $error[] = 'Only CSV files accepted!';
    }
    if ( ! $error ) {
        $tot    = 0;
        $handle = fopen( $_FILES["service_upload_csv"]["tmp_name"], "r" );
        //echo $file   =  $_FILES["service_upload_csv"]["tmp_name"];
        while ( ( $data = fgetcsv( $handle, 1000, "," ) ) !== false ) {
            for ( $c = 0; $c < 1; $c ++ ) {
                //only run if the first column if not equal to firstname
                if ( $data[0] != 'Department Name' ) {
                    $insert_csv_query = "INSERT INTO wp_services(
                                dept_name,
                                inc_10_codes,
                                description,
                                uc_fee
                                            )VALUES(
                                '" . mysql_real_escape_string( $data[0] ) . "',
                                '" . mysql_real_escape_string( $data[1] ) . "',
                                '" . mysql_real_escape_string( $data[2] ) . "',
                                '" . mysql_real_escape_string( $data[3] ) . "'
                                )";
                    $insert_csv_query;
                    $inserted = $wpdb->query( $insert_csv_query );
                }

                echo $tot ++;
            }
        }
        fclose( $handle );
        $_SESSION['pd_services_total_import'] = $tot;
        wp_safe_redirect( admin_url( 'your admin url here' ) );
    }
 }
}
add_action( 'wp', 'process_pd_services_upload' );

In the redirected page you can display message from the $_SESSION['pd_services_total_import'] an then unset( $_SESSION['pd_services_total_import'] )