The WP Super Cache plugin was seriously affecting my WooCommerce store (with a WooTheme).
For example, I tried updating the text on the site's banner — a thing from the theme on the homepage, and it would not change. Once I disabled the banner completely, the store slowed down miserably. Even the WP backend wouldn't load properly.
Disabling WP Super Cache fixed it.
Seems that it doesn't get along with WooCommerce/WooThemes. Or is there something I should have done?