Look at the ADXL data sheet under the absolute ratings and see if it can stand the extra voltage, I would suspect that it can't.
Regulating 3V3 down to 3V is a bit tricky even for a low drop out regulator you would be much better off regulating it from the 5V line. Besides the 3V3 from the Arduino has only a very limited current capacity (less than 50mA I think)
Data sheet says the range is 1.8 - 3.6 V. I have a similar one from ADXL (335) and am using it just fine on an adafruit breakout board.
The output voltage is ratiometric, which means it is proportional to the source voltage.
In my application, I do a zero g calibration at the beginning to establish what the output voltage level is when the chip is at rest, before starting to read the data. This is used as an offset for all other readings.