Diamond cuts silicon just fine.
The suggestion of using a tile saw is a good one, but whatever approach you take, you will get some chip-out around the cut. Silicon is as brittle as glass, with similar issues with regard to splinters. Silicon splinters are very sharp and hard to dig out of your skin (I know this for a fact). Silicon splinters will slowly dissolve in your finger and are infection-prone, so cutting silicon with water lube is a really good idea. You most definitely don't want to breathe silicon dust.
A 6 x 6 x 8 inch chunk of silicon must be a remnant from a silicon wafer manufacturer. Maybe the end of an ingot? I can't imagine any other industry that would be interested in hunks of pure silicon that size.
When a piece of silicon is placed in direct sunlight it can get very hot. This is because it absorbs light in the visible spectrum, down to about 1 micron wavelength (a bit below our perception of dark red) -- but it is transparent to longer wavelength light, as in the thermal IR region. This means it cannot emit long-wavelength IR, so it just gets hotter and hotter until heat loss by convection balances the thermal input. The 1 micron cutoff also is the reason why CCD or CMOS cameras can't "see" light below 1 micron -- no light absorption so no photo-current. Thermal-IR cameras use different semiconductors, or totally different detection technology like bolometer arrays.
