Most obsidian is going to be harder than the lead glass crystal or ceramic glaze on other dining ware, though. It (and many other gemstone materials) does tend to scratch when thrown into a jewelry box with mixed hardness gemstones, knocked around a lot or polished with pads contaminated with tiny bits of harder stuff. Soaking in strong coffee would be a good idea. Things like copper sulfate or cupric chloride (you can find in concrete stains at your masonry center) act faster to show how a material will uptake staining agents - amazing how fast some stuff you'd think was impermeable will soak up color.
If the cup is not going to be used for drinking or holding liquids, alabaster and soapstone are easy to carve. Alabaster has a nice semi-translucent glow, comes in affordable blocks in varied patterns/colors and takes a nice polish. Both get made into cups, bowls and dishes - but do have to be sealed and even then don't do well with staining, which is why I brought up that concern. Marbles are similar, but a bit harder. Rhodonite, labradorite, sodalite, tigereye, fluorite, milky & rose quartz and petrified wood can be found in block form. For something tougher to carve, but tougher to break, quartzite and nephrite also come in block form. Did you get any Polka Dot in a chunk large enough for a mug? The folks at Richardson's do cores of various materials for spheres, and the smaller cores would work for a mug. Might be worth a trip back there if you can recall something they had on-hand that would work. Healed formation fractures and veils in quartz, agate and similar material are pattern, and shouldn't affect the stability of your piece.