It is the theme that should be responsive. And if the theme is responsive and it supports WooCommerce, then the theme is responsible to make WooCommerce responsive as well...
This sounds good but WooCommerce is still not working very well with a stock theme (TwentyThirteen).
Just pull up the Cart page on an iPhone 5/5s using the TwentyThirteen theme and you can see the layout is somewhat broken. When TwentyThirteen works as designed, you should not see everything pushed the left with white space running from top to bottom on the right. Yet, that's exactly what the Cart page is doing.
This is exactly what happens to TwentyThirteen when any posted content is wider than it should be. The Cart page itself is just too wide for this theme on iPhone.
Again, this example only uses default installations of TwentyThirteen and WooCommerce... nothing modified.