Great question. Lately, the teacher has been throwing more new stuff at me; I usually average only one new piece a month (I've been playing less than a year, mind you.)
I do strategize how to get to the new piece and not lose the old ones.
So I warm up sometimes on a new-old piece (my last "finished piece was a Savio lullaby, so I now start with it to warm up) and then puzzle through the new work. First I see if I can sight read it. I mark any trouble spots or where the notation hasn't said anything about string position when it's obvious I would need Spider-Man hands to play in first position. I mark the spot where I can't play it at all. Then I break the thing down and play measure by measure or if it's easier, section by section, often w metronome. Then I have to mark in dynamics because instructor glares if I play anything with zero musicality even three minutes after my first lesson. After the first run through, I do any exercises we've cooked up for the new piece before playing it.
As the weeks go on, I put that piece first in practice so I can memorize it (I memorize all my stuff because I hate using bifocals and a music stand, the joys of aging) and because it makes it easier for me to concentrate on the musicality. I make notes where I'm goofing up, after lessons and then record on my phone to hear any issues and progress.
On other practice sessions, I'll play through my entire "repertoire" such as it is (about a dozen pieces, maybe at this point) and every other practice, I'll start with whatever scale I'm trying to get proficient on and play that first or only, so I don't neglect it for the fun stuff.
I find it helps to have intentional practice, where you set a goal (this measure, that fingering, better dynamics, etc) and try to accomplish one thing really well.