There are two ways other rocks can be formed. The first is when a new episode of mountain building creates intense temperature and pressure regimes that melt or destroy the original granite. When the new rock cools, it solidifies with the same chemistry but with a new mineral composition. Granite is a silicate, so any rock formed can only be a silicate, such as: quartz diorite, gabbro and andesites possibly with the addition of crystals of olivine, garnet or pyroxenes. The new rock will almost certainly contain quartz as this is the first silicate mineral to cool in these processes.
The second way that other rocks can be formed from granite is by erosion and sedimentation. This method preserves the original composition of the granite mineralogy but breaks each component down into small particles and then compacts them or washes them away depending on the geomorphological processes involved. Geomorphology is the study of the changing nature of rocks on the surface by a process known as weathering, which will be either a chemical process or a mechanical process.
Chemical weathering breaks down granite by corroding the feldspar content when it comes into contact with acid and water on the Earth's surface. Feldspar weathers to clay which will eventually be compacted to form shale. The commonest form of mechanical weathering of granite is freeze/thaw, which occurred during the Earth's ice-ages. In this process, water enters the cracks in granite and freezes. When it does so it expands, opening up the cracks further until the rock eventually breaks into pieces.
Quartz is generally the first mineral to cool in igneous rocks with a silicate base. It is also the hardest mineral present in granite, whereas biotite is the softest. The mechanical erosion process destroys the biotite but not the quartz. Chemical weathering destroys feldspar. Because granite is a silicate, there is no calcium in its composition so it can never form sedimentary limestone. For all these reasons, the most common sedimentary mineral in the Earth's crust is sandstone made up largely of quartz.