Upon breaking apart andesite, what do you get?
By definition andesite is mainly plagioclase (mostly variety andesine),and pyroxene with either quartz or olivine (not both), and minor amounts of magnetite, ilmenite, zircon, apatite, possibly biotite mica, and maybe a few traces of rarer minerals. The pyroxene is probably a mixture of orthopyroxene and augite. In addition to plagioclase there may be small quantities of other, more alkaline feldspars.

Andesite is chemically about 60+/-3% silica, SiO2, but the amount of free silica is very small, if present at all - at most 2 or 3 percent. So no, you won't extract commercial powdered silica. Better than 99.9% pure silica is found very abundantly in some quartzites, a common sedimentary rock. So nobody is going to try to extract silica from other silicates.