If you have a MacPro, you have space for three more internal drives in addition to the system drive. Copy your footage to one of the other drives, assuming you have them installed. Relink and try it. An internal SATA drive should be able to do two streams of video without issue assuming you aren’t cutting something like Red footage.
USB external drives won’t work reliably.
Drives are pretty cheap and install in about 5 minutes or less. If you add new drives, make sure they are formatted for Mac before trying to use them.
E=MC2+/-2db