When discount coupon code amount is greater than cart order total, calculated order total is wrong. For example coupon code amount is $40.63 and cart order total is $35.95. Here are two steps to fix this problem. In ot_coupon.php make these changes.

1. In function calculate_deductions function comment one line.

           if ($coupon->fields['coupon_type'] == 'P') {
            $od_amount['total'] = round($orderTotal*($coupon->fields['coupon_amount']/100), 2);
            $od_amount['type'] = 'P';
            $ratio = $od_amount['total']/$orderTotal;
          } elseif ($coupon->fields['coupon_type'] == 'F') {
            $od_amount['total'] = round($coupon->fields['coupon_amount'] * ($orderTotal>0), 2);
            $od_amount['type'] = 'F';
            $ratio = $od_amount['total']/$orderTotal;
          }

          // comment this line so that the actual coupon amount is propagated.
          //if ($od_amount['total'] > $orderTotal) $od_amount['total'] = $orderTotal;
          //
          switch ($this->calculate_tax) {
            case 'None':
              if ($this->include_tax == 'true') {
                reset($order->info['tax_groups']);
                foreach ($order->info['tax_groups'] as $key=>$value) {
                  $od_amount['tax_groups'][$key] = $order->info['tax_groups'][$key] * $ratio;
                }
              }
            break;
            case 'Standard': ...

2. Comment three lines in process function

  function process() {
    global $order, $currencies;
    $order_total = $this->get_order_total();
    $od_amount = $this->calculate_deductions($order_total['total']);
    $this->deduction = $od_amount['total'];
    if ($od_amount['total'] > 0) {
      reset($order->info['tax_groups']);
      $tax = 0;
      while (list($key, $value) = each($order->info['tax_groups'])) {
        if ($od_amount['tax_groups'][$key]) {
          $order->info['tax_groups'][$key] -= $od_amount['tax_groups'][$key];
          $tax += $od_amount['tax_groups'][$key];
        }
      }
      if ($od_amount['type'] == 'S') $order->info['shipping_cost'] = 0;
      $order->info['total'] = $order->info['total'] - $od_amount['total'];

      //comment these lines
      //if (DISPLAY_PRICE_WITH_TAX != 'true') {
      //  $order->info['total'] -= $tax;
      //}

      $order->info['tax'] = $order->info['tax'] - $tax;
      //      if ($this->calculate_tax == "Standard") $order->info['total'] -= $tax;
      if ($order->info['total'] < 0) $order->info['total'] = 0;
      $this->output[] = array('title' => $this->title . ': ' . $this->coupon_code . ' :',
                              'text' => '-' . $currencies->format($od_amount['total']),
                              'value' => $od_amount['total']);
    }
  }

Finally check discount coupon configuration in admin to make sure it does not include shipping.