Is there any way to exclude the styling of certain elements from being
No. CSS is not that complicated.
I am assuming that you are creating a child theme. If so, what you can do is
enqueue the parent, Twenty Thirteen stylesheet before you enqueue your child stylesheet. Then, any selectors listed in the child that match selectors in the parent will override the parent. The advantage of that over the solution by simply copying the parent stylesheet is that it should be more robust over time. Imagine that the markup of the parent changes. If you've copies the stylesheet meant for an older markup, you may have a stylesheet that is broken by beinig out of sync with the markup.
The disadvantage is that you will be loading more CSS than you need to be, maybe a lot more.
You can also just write your CSS rules to have more specific selector than the parent.