I had students facing this same problem. We had a file called BigBend in geographic coordinate system GCS_WGS_1984. Note that the units are in Degrees.
Take the unprojected elevation raster and use the Raster Calculator to create a Raster Attribute Table.
int(BigBend_dem.tif)
... new output something like BigBend_INT
The reproject the new file into UTM.
Project Raster - give it a new output file name (BigBend_Proj), set the resample technique to Cubic (NOT nearest) THEN
set the output to Projected Coordinate System > UTN > North America > Nad1983 HARN UTM Zone XX (whatever your UTM zone is).
Now try running the slope tool and let me know if that works.