I would recommend opening up a support case with the support team for this. There could be many items leading to memory and disk space utilization. Simply having an undersized server can lead to this as well. One thing you can try is a tabadmin cleanup this will clear unnecessary logs and other temporary files.
The online help for server provides some steps for troubleshooting disk space usage: Troubleshoot Disk Space Usage on Tableau Server Nodes
In addition to log files, you need to use the canned admin views provided by Tableau Server to monitor disk space usage by user, project, workbook and data source: Stats for Space Usage
You also need to ensure that you are maintaining Tableau Server's internal database as recommended: Database Maintenance
You can use tabadmin cleanup command to remove unnecessary files from tableau server.
This increase the space on the 'c' drive and also improves the performance of tableau server as well.