The experience of using tables in websites whilst on a mobile can be pretty poor. Things tend to get a bit squashed and displaying the information can be a challenge just to fit the table onto the screen.
I was recently faced with a similar problem where I had a particular design in mind for the mobile version of the table. The solution I found was base based on some responsive table designs from CSS-tricks. I'm certainly no designer, but the what I created worked for the situation I was trying to solve.
The basic idea is that instead of treating the table like a table, change all of the table elements to block elements when displaying on mobile. This meant that when viewing the table in a mobile view it would be rendered in a different way, allowing it to be shown in a mode that was more mobile friendly.
Let's use the following table filled with some data.