That is a bit tight on space, and the problem you are seeing is just that running out of room to do the swapping and memory paging operations. This will affect your machine performance overall so you may want to consider this if possible.
You can run applications from external drives, however, that may come with a performance hint due to USB being much slower than SATA. If your machine supports E-SATA (External- SATA) drives, you can then use those with little or no performance hit. If your system supports the new Thunderbolt interface, you maybe even better off since that is supposedly faster still. I have not used them to know if this is true or not, just read about the interface.
With TransDEM, you can specify a different location, such as your external drive to hold your data and keep the application on the smaller internal drive, however, you do need a bigger internal drive if you can do that. I currently have my TransDEM Data, which includes the downloaded DEMs, projects, and exported routes on a separate drive away from my much smaller SSD which holds only my programs and OS.
John