Can I use GSM and Data Logger Shield at the same time on one Arduino?
It depends, but high likely yes.

The sensors, GSM and Data Logger may use the I2C, SPI, analog pins or UART (last not likely).

For I2C, the Arduino can handle many of such devices, because it is part of the protocol.

For SPI it is similar, although some cheap SD card reader for Arduino are notorious not being compatible with other SPI devices. And the Arduino has only one SPI port (but can handle many SPI devices, as long as they all are capable to allow other SPI devices).

For analog pins, these are likely only used by sensors, the Arduino has 5. But there are some ways to use more sensors by polling, using multiplexers etc.