Hide or minimize (not force kill or quit) a temporarily frozen or stuck program window?
I'm tempted to post this as an answer, even without full info…

I am assuming that if you cannot  Cmd ⌘   Tab ⇥   to another app at this point, it is because the entire machine is currently too busy to respond, not just the frontmost app.

If an app itself is unresponsive [&amp; you can see other apps around/behind it, i.e. not full screen or maximised], you ought to be able to simply move the cursor outside that unresponsive app &amp; the daisy wheel will go away, returning to the standard cursor. Clicking one of the other apps will bring it to the front.  Cmd ⌘   Tab ⇥   at this point would also work.

If the daisy wheel doesn't go away outside the borders of the unresponsive app, then the entire machine is too busy to respond - usually just temporarily, until whatever process taking all the resources has finished its task.

Photoshop processing a very large image for the web is just the kind of task that can temporarily use large amounts of RAM &amp; CPU. I just tested on a 5000 x 3000 image. Photoshop went busy for approx 15s, RAM usage doubled &amp; CPU usage went to 100% [which is 1/24th of the number of virtual cores I have, so in essence used one core to its fullest] . I was able to change screens, switch to other apps etc, but I'm running on a 12-core Mac Pro with 64GB RAM.  

From this snapshot you can see the brief effect [highlighted in red] on the cores &amp; the drop to 'not responding' in Activity Monitor.
Perhaps try some comparison tests &amp; see what figures you get at the same point.