Many pedals cut bass by default. In fact, the EQ in pedals along is a WHOLE topic of discussion that could go on forever. However, it's VERY important and some understanding of it goes a long way in helping you find which ones work best for your tastes and gear.
As J said, this is a deep subject. So I'll just add a quick one for now. What the Timmy does that is so smart, is that it removes bass from the circuit pre-clipping. It's well know that overdrive circuits don't handle bass well. What the Timmy does that is so slick, is remove it pre-clipping, and then add it back in afterwards with a control to dial how much you add back. The end result is that you can cut some, or alot, or even end up boosting it, but whatever bass you add back has NOT gone through the clipping circuit. This is brilliant and the end result is outstanding. Even if you do put all the bass back that you took out up front of the circuit, it would be cleaner, tighter, punchier, etc.
At one point in my pedal building/modding days, I was going to get a scope and run a flat signal through various pedals and run frequency plots on the outputs, to show just how much these pedals vary. And...
YES, there are many types and levels of clipping that influence the sound, but IMO, these frequency differences are often MORE important than that, in our decisions of what works best for our tonal preferences and gear. Think about it. (Or just play with a graphic EQ in front of your amp!) When you shape the frequencies before they go into a tube amp circuit, it changes many things about how the amp itself reacts to your playing. Cutting or boosting bass, treble or mids, and the center frequency of the control in question, significantly changes how an amp responds, clips, etc.
Oh wait, this was going to be a quick reply.