How to remove td border with html?

To remove borders between cells, while retaining the border around the table, add the attribute rules=none to the table tag.

There is no way in HTML to achieve the rendering specified in the last figure of the question. There are various tricky workarounds that are based on using some other markup structure.

simple solution from my end is to keep another Table with border and insert your table in the outer table.

<table border="1">
    <tr>
        <td>
            <table border="0">
                <tr>
                    <td>one</td>
                    <td>two</td>
                </tr>
                <tr>
                    <td>one</td>
                    <td>two</td>
                </tr>
            </table>
        </td>
    </tr>

</table>