Does Mr. Mime's "Scoop-Up Block" Ability prevent Recycle Energy or U-Turn Board from going back in to the hand?
Yes, it does.
Source: TPCi Rules Team (2019-08-01)

Relevant cards

Note: All applicable cards may not be listed below.
SM11_211
SM11_211
SM11_212
SM11_212
SM11_255
SM11_255
SM11_257
SM11_257
SM9_66
SM9_66