Primes slow performance was criticized here quite some times, but as far as I can remember no significant solutions could be offered.
In some cases vectorized operations were said to help speeding up calculation
https://community.ptc.com/t5/Mathcad/Mathcad-Prime-8-is-very-slow-Tips-or-tricks-to-increase-speed/m-p/840078/highlight/true#M203877
and Vladimir once posted links to a few KB articles but I have not looked at them in detail and am not sure if they would be of much help
https://community.ptc.com/t5/Mathcad/Mathcad-prime-8-0-0-0-slow/m-p/838905/highlight/true#M203777
I don't think that file size itself really is an issue. If the size of the saved file should be decreased you may consider deleting \mathcad\result.xml in the file after saving (mcdx files are just renamed zip files containing a certain file and subdir structure). The result.xml is used to be able to display the results of the last calculations after the last saving when the file is loaded (no automatic calculation on start up as we were used in legacy Mathcad). If its not present, Prime will start to (re)calculate the sheet after loading the file, similar to the behaviour of legacy real Mathcad. Deleting result.xml will not help concerning speeding up the handling and calculation of the Prime sheet - it will just decrease the size of the saved file and as I already said, I don't think that thats an issue.
You may try to get rid of the embedded Excel-component and instead read-in the data from an external Excel sheet using READEXCEL. It sure will decrease the file size (but you would have to manage a separate Excel file) but thats not the point. Using READEXCEL does not need and start Excel itself in the background and so will be faster after loading the worksheet and while I had only glanced over the links ValeryN had posted I saw some issues mentioned with embedded Excxel sheets. So I thought it might be worth a try. I won't expect any improvements concerning the subsequent filtering and submatrix manipulations you describe, but who knows ...
Concerning the usage of clear() I guess you are on your own to experiment and give it try. I can't remember that it was ever mentioned that it would affect file size or speed. But we don't know how memory management and garbage collection is implemented internally in Prime, so its a matter of trial an error.
I also found a thread where someone reported that a solve block fails if Multithreading is enabled and would work OK if its turned off (he was not able to post the sheet). Furthermore the user reported that turning off Multithreading speeds up calculation time for him. But that thread was one in the early days of Prime and I guess that Multithreading in the meantime was fixed and improved by PTC. Multithreading sure adds some overhead which costs time, but if the sheet contains independent threads which can be calculated in parallel it sure should speed up overall calc time by using more than one processor core. But again - you have to give it a try.
Good luck!