How to subtract out the slope (in general) of a DEM?

I'm searching for a solution process to subtract out the slope of a DEM like this:

I have a high resolution DEM and want to reconstruct historical/old/not active parts of a river. The problem is the trend of the whole area. Structures from different areas are at different highs and its not possible to describe/visualize the whole area in the same way. So my idea is to adjust all highs to solve the problem.

Any idea? For this issue the surface tools within ArcMap are seeming useless to me.