(This answer is based on my experience with mathematical writing. I assume that it should apply to other kinds of scientific writing too, but your mileage may vary.)
I suspect that you may be fundamentally misunderstanding the purpose of the writing that you are having a hard time "discarding".
It seems like your logic is that you spent a lot of effort writing a certain paragraph, but since the paragraph will not appear in the final version of your manuscript, this effort was wasted. So that the effort is not wasted entirely, you would like to keep your writing in the drawer so that you can pull it out later at an opportune moment. This is of course pure speculation on my part, but I cannot imagine why else you would "find it difficult to discard old writing".
The flaw in this logic is the idea that the effort it took to write the paragraph will go to waste unless you use it somewhere. This is a misunderstanding. The effort was not wasted, since the paragraph has already served its purpose, which was to serve as a stepping stone on the path towards the final manuscript. Its purpose is not to be something for you to hold on to until you find a proper place for it. The paragraph had its place in the process of exploring and stumbling towards the final manuscript, but after it has served that purpose it's time to let go of it. Imagining that it is going to be revived for some other purpose is almost always wishful thinking.
Of course, from time to time you may find yourself writing an outstandingly well-polished couple of paragraphs which for some reason or another did not quite fit into the final manuscript, or paragraphs where you have a convincing, well-articulated reason to believe that they might be useful later, rather than a generalized feeling of what if. These it makes sense to keep around. But your average run-of-the-mill paragraphs that simply didn't make it through the editing process? Kill them and don't carry their corpses around. (This does not mean that you should never back up previous versions of your work, but rather that you should not primarily do so with a view to resurrecting unused paragraphs in some future work.)
Your stated reason for keeping these paragraphs in a state of suspended animation is "so you don't have to rewrite the same paragraph in future". Again, I suspect that there is some fundamental misunderstanding here, because it's not like the act of writing a paragraph is a major undertaking. The amount of effort you are going to save by not starting from zero is going to be infinitesimal, and is more than made up for by the fact that writing the paragraph anew will almost certainly result in a better one. What is a major undertaking is polishing a paragraph over and over again (and moving it to and fro) until it fits perfectly into its surroundings. But this process is not something you can substantially speed up by cutting and pasting bits and pieces from your previous work. Whether you start from zero or not is almost irrelevant, as long as your focus is on producing good writing rather than spending a minimum amount of effort on the writing process.
I can sympathize with the fact that at the beginning of your scientific career it make take you some time and effort to write a coherent paragraph, so my comment that the amount of time saved is going to be infinitesimal might not ring true to you. If so, then that's all the more reason for you to practice the bread and butter of scientific writing – which is editing, rewriting, and experimenting with different ways of expressing the same idea, rather than clinging to existing strings of words and sentences – until it does ring true.