This sounds to me like a project that would be much better suited to a Raspberry Pi.
When you switch to Voice Receive mode what stuff do you expect to appear from the modem? My guess is that it will be an audio signal that could be heard if connected to a loudspeaker.
An Arduino's USART is not designed to receive anything like that. It is only designed to receive digital signals in a specific format.
Perhaps you could use a jumper to connect the output from the modem to one of the Arduino analog input pins and use the ADC to sample the signal. But the ADC is not very fast so the quality will probably be very low. And IIRC telehone audio used to be filtered to reduce the required bandwidth so you may be getting a poor quality sample of a poor quality signal.
Writing to an SD Card is also relatively slow.
...R