Issue with Clipping a Shapefile to Mosaic

Hello,
I am trying to clip a stream to my mosaic layer. But it’s not working.
I downloaded all my data from USGS. I created the mosaic file out of the several img files (DEM) following this instruction:
ArcCatalog > New Geodatabase > Rightclick > New Mosaic Dataset > Rightclick > Load data > and picked all my img files as input.
Afterwards, I opened a new ArcMap file and added the mosaic layer I had created in the previous step.
The ways I tried to clip:
1) Used the Geoprocessing tab > Clip > but the Mosaic layer wouldn’t show on the “Clip Feature” (or “input feature”) section.

2) ArcToolbox > Raster > Raster Processing > Clip

But with this path, the only thing that I can do is Clip the RASTER to the Shapefile. I want to do vice versa.

Could anyone help me with this issue please?

p.s. I tried to make a polygon out of my mosaic so that I use the polygon for clipping, but I couldn’t get it to make the polygon. Toolbox > Conversion Tools > From Raster > Raster to Polygon > input my mosaic file but it gives me the following error:
ERROR 000864
Input raster: The input is not within the defined domain. ERROR 000863: Invalid GP data type