Commerce Line Item Taxonomy Reference Filtered by Product Selection
You have two basic approaches you can use: either treat the stain color as a customization or treat it as a second attribute.  Which you pick depends on a little on your backend process needs and the experience you want to provide.

If you use a second attribute and have a product variation for each stain in each wood, Commerce's default add to cart form should provide the user experience you are describing. You might find it helpful to take a look at this tutorial.

If you want to treat stain as a customization you'll likely want a couple extra modules -- in particular Commerce Customizable Product.  Commerce Guys have a tutorial covering that scenario.