The TFT driver chip can be put into a low power state, but the the big power consumer on these displays is the backlight LEDs which take in the range 100-200mA. Typically these LEDs are wired straight to the power pins of the Arduino, so the only way to power off the display is to add a transistor switch.
If you do this then you need to ensure all control/data output lines are also put into a high impedance state (turned into inputs) otherwise the data lines will provide power to the board and be overloaded.
So your options are limited to: change your display to an OLED (expensive for large colour displays) or have two Arduino's, one being completely powered down by another, say a Pro Mini.