Hi,
In order to make your table scrollable you have to use the "slds-scrollable" in the tbody where you are showing the records in the table and to do it without datatable please consider the following example:

<table class="slds-table slds-table_cell-buffer slds-table_bordered">
  <thead>
    <tr class="slds-line-height_reset">
      <th class="" scope="col">
        <div class="slds-truncate" title="Opportunity Name">Opportunity Name</div>
      </th>
      <th class="" scope="col">
        <div class="slds-truncate" title="Account Name">Account Name</div>
      </th>
      <th class="" scope="col">
        <div class="slds-truncate" title="Close Date">Close Date</div>
      </th>
      <th class="" scope="col">
        <div class="slds-truncate" title="Stage">Stage</div>
      </th>
      <th class="" scope="col">
        <div class="slds-truncate" title="Confidence">Confidence</div>
      </th>
      <th class="" scope="col">
        <div class="slds-truncate" title="Amount">Amount</div>
      </th>
      <th class="" scope="col">
        <div class="slds-truncate" title="Contact">Contact</div>
      </th>
    </tr>
  </thead>
  <tbody>
    <tr class="slds-hint-parent">
      <th data-label="Opportunity Name" scope="row">
        <div class="slds-truncate" title="Cloudhub">
          <a href="javascript:void(0);" tabindex="-1">Cloudhub</a>
        </div>
      </th>
      <td data-label="Account Name">
        <div class="slds-truncate" title="Cloudhub">Cloudhub</div>
      </td>
      <td data-label="Close Date">
        <div class="slds-truncate" title="4/14/2015">4/14/2015</div>
      </td>
      <td data-label="Prospecting">
        <div class="slds-truncate" title="Prospecting">Prospecting</div>
      </td>
      <td data-label="Confidence">
        <div class="slds-truncate" title="20%">20%</div>
      </td>
      <td data-label="Amount">
        <div class="slds-truncate" title="$25k">$25k</div>
      </td>
      <td data-label="Contact">
        <div class="slds-truncate" title="jrogers@cloudhub.com">
          <a href="javascript:void(0);" tabindex="-1">jrogers@cloudhub.com</a>
        </div>
      </td>
    </tr>
    <tr class="slds-hint-parent">
      <th data-label="Opportunity Name" scope="row">
        <div class="slds-truncate" title="Cloudhub + Anypoint Connectors">
          <a href="javascript:void(0);" tabindex="-1">Cloudhub + Anypoint Connectors</a>
        </div>
      </th>
      <td data-label="Account Name">
        <div class="slds-truncate" title="Cloudhub">Cloudhub</div>
      </td>
      <td data-label="Close Date">
        <div class="slds-truncate" title="4/14/2015">4/14/2015</div>
      </td>
      <td data-label="Prospecting">
        <div class="slds-truncate" title="Prospecting">Prospecting</div>
      </td>
      <td data-label="Confidence">
        <div class="slds-truncate" title="20%">20%</div>
      </td>
      <td data-label="Amount">
        <div class="slds-truncate" title="$25k">$25k</div>
      </td>
      <td data-label="Contact">
        <div class="slds-truncate" title="jrogers@cloudhub.com">
          <a href="javascript:void(0);" tabindex="-1">jrogers@cloudhub.com</a>
        </div>
      </td>
    </tr>
  </tbody>
</table>

Please go through the following links if you need more information about the scrollable class and table:
https://www.lightningdesignsystem.com/components/data-tables/
https://www.lightningdesignsystem.com/utilities/scrollable/

I hope you find the above solution helpful. If it does, please mark as Best Answer to help others too.

Thanks and Regards,
Deepali Kulshrestha.