Instructions
Turn on the Xbox 360 console. Navigate to the My Xbox screen within the dashboard and then select "System Settings."
Scroll down to the "Memory" option on the System Settings menu and press the "A" button on your controller. This will bring up a list of all connected storage devices for your Xbox 360 console.
Highlight the "Hard Drive" option and then press the "Y" button on your controller to enter the Device Options. Select the "Clear System Cache" option and then select "Yes" when it prompts you to begin performing maintenance.
Wait until the maintenance is complete, which will take a few minutes. Once complete, your system cache will be cleared, which should resolve any hard-drive slowdown.