Yes, the Wolfram library can export MXNet architecture and weight files:

https://reference.wolfram.com/language/ref/format/MXNet.html

There are open source libraries that can convert MXNet models to tensorflow models.

Also, there is newer support for ONNX model exports, but I have never tried this myself. ONNX has importers from all the major neural network libraries (tensorflow, pytorch, etc.)

https://reference.wolfram.com/language/ref/format/ONNX.html

Lastly, if you want to process big datasets with Mathematica, I have found this is possible if you ditch the GUI and stick to writing scripts (.m/.wl files) and running them with the wolframscript -f command line utility - like you do in python. The Wolfram/Mathematica Desktop GUI is definitely too slow - and crashy- for a lot of 'real' problems with large datasets right now :(

Are you sure? I think I saw a video of how to process extremely large data (tens of GBs) using the Wolfram desktop. Its not done with Import though.

Edit (in 2022, WL v13.1), it appears that several of these issues have been fixed. The NetTrain progress reporting graph no longer makes the Documentation UI completely unusable, re-running NetTrain in the same WL kernel no longer causes GPU memory to build up, and the training progress graph interface seems generally more performant and less crashy. Thanks for the updates, WRI!