Yes, by using the DJ software’s recording function.

Input the (digital) sound output from the DJM-850 to the DJ software on the computer. (USB sound card function)

For details on setting the sound output from the DJM-850, see “About the driver software and setting utility software” – “About the setting utility software” in the operating instructions. For the settings in the DJ software, see the DJ software’s operating instructions.

The sound can also be recorded by connecting the REC OUT terminals to a recorder equipped with analog input terminals.