How do you get hard edges after deleting in the spectral display??

The real reason that this won't work is that to implement that response in a digital filter would make it ring severely at the edges, and it would require a significant processing overhead in the filter itself to achieve it anyway. It would serve no useful audio purpose either. It has nothing to do with the sample rate, or anything like that - it's a filter limitation. It's true that if you zoom out, it's easier to achieve what looks like a sharp edge, but if you zoomed back in again, you'd still see the blur. Also you can alter the visual effect of what you can see by altering the FFT size of the display - but once again, if you reset it you'd be right back where you started from.

If what you're doing requires it to sound a specific way, I'm not sure, but if you just want to add hidden images for easter egg purposes, I think you could zoom out and try it then. The reason it's blurry is because the audio "resolution" (sample rate) isn't enough to produce the clear sharp edges you want when you actually cut the desired frequencies from the clip. It would be like zooming in into an image and trying to cut shapes into the pixels.
Zoom out so you can work on an area of, say, 4-5 seconds, and also zoom out vertically (with ctrl+mouse wheel) so that the top squishes the bottom and your shapes should look sharper.