If it's during the writing (not compiling the finished document I mean), you can speed-up the compilation ! Tips (not sorted) :
Split the doc into multiple files and use \include for each file (e.g. chapters), and comment out the ones you are not working on (so you are only compiling the chapter you are working on)
Use latexmk (to cache results) and please use a better engine (I started with XeLaTeX and it was great, and I now use LuaLaTeX for some documents requiring special processing, or using multiple heavy fonts). You can also use it to parallelize some operations !
Since you're making diagrams, I'll assume you're using TikZ. I love TikZ. Did you know you can cache TikZ diagrams too ? They call it externalizing, just \usetikzlibrary{external} followed by \tikzexternalize[prefix=diagrams/] to avoid reprocessing every diagram (in the preamble)
Use less packages ! When I started LaTeX, I had a long list of packages I sometime used and that were handy (so I didn't need to add the package, I could just write and not think about it). But packages are processed, so remove the useless \usepackage (worst ones being fontspec (which you don't necessarily need) and TikZ; probably minted too but I switched to listings). Same goes for TikZ libraries. Also you don't need inputenc if using a modern engine, we all use UTF-8 anyway... I hope.
If you're using images, compile in draftmode to avoid processing them (you'll do it later). Same goes for hyperref. Just pass the option draft when loading graphicx or hyperref, or in the \documentclass (or use the appropriate flag with you compiler)
Some niche ones I don't use, but for big projects (hundreds of pages and tens of figures), you can
You can also preprocess the preamble once (don't forget to recompile when updating it tho).
Same for bibliography, don't recompile it if it hasn't changed
Optimize (compress) your pictures if you have some (although, if using draft mode, not an issue)
Compile less (some editors auto-compile to emulate WYSIWYG, same for latexmk with the -interaction=nonstopmode flag; disable it).
Use batchmode to remove the output, it's not a lot, but still.
If desperate, reduce PDF compression until the final compile (xdvipdfmx -z0 produces heavy files, so stick to -z2 or -z3, it'll be noticeably faster but still produces medium sized files). You can also configure it in the preamble, using \pdfcompresslevel=2 and \pdfobjcompresslevel=2
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