Everybody knows the issues with TablePress, legend says there is a paid version of it with fixed this.

But for us the following workaround should be okay.

Use the following code on your table in your article:

<div class="tablepress-wrapper">[table id=1 /]</div>

And then add the following CSS code to your Tablepress custom CSS setting:

.tablepress-wrapper {
	overflow-x: scroll;
	overflow-y: hidden;
}

There you have it, when you know make Tablepress fixed width (or bigger with dynamic values), it will overflow in another tiny window as if it was an iframe.

Have fun