Does shaking iPad violently going to damage its orientation hardware?
The iPad Mini's accelerometer is a solid-state (with a microscopic mechanical - thanks Graham Parks for the correction) device so shaking should not hurt it. Electric shocks (for e.g. immersing iPad in water while it's on) and heat do damage electronics.

You're more likely to break the adhesive that connects the gorilla glass to the aluminium back before hurting the accelerometer.