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I'm currently playing a piece which requires big stretches of large intervals across the keyboard. It slightly hurts when I do so, and I am wondering if I should continue to practise like this.
My piano teacher suggests fingerings with a combination of 3 1 and 2 1 in the L.H.
Don't persist in doing anything that hurts.
As commented, if you show us the passage in question we might be able to suggest a strategy.
It slightly hurts when I do so
Huge cue! You should never ever insist with something that hurts and that could damage you in any way. If somebody recommends some kind of exercise, but when you do it, it hurts, the exercise just isn't right, or you are not doing it right, or the exercise doesn't work for you. Either way, you should never go through pain to achieve anything.
So, shortly:
I am wondering if I should continue to practise like this.
No.
Sadly, some piano music simply can't be played as written with small hands without some modification. If you're trying to play certain pieces by, say, Liszt or Rachmaninoff (two famously large-handed performers - seriously, they still make plaster casts of their hands so you can compare to an average human - they're enormous), you may not be able do as wide a spread as they could, and so some music they wrote may be physically beyond your capability. There are exercises you can do to increase your hand span, but they can only take you so far. You may find you need to roll chords rather than play all the notes at once, or even omit or transpose some notes if your hands cannot reach them all. Many publishers include suggested variations for small hands on some difficult passages.
Since we can't see the score, and we don't know exactly what you are trying to do, it's hard to answer this, except by saying:
Whatever you are doing, it is the wrong technique to play the piece, so stop doing it before you injure your hands permanently.
In my piano lessons I was told the story in which famous composer Schumann permanently damaged his fingers by performing excessive stretching exercises:
(...) that Schumann damaged his finger by using a mechanical device that held back one finger while he exercised the others—which was supposed to strengthen the weakest fingers
(From Wikipedia)
This story (I really see it as a story, I think it's historically unproven) was told to me to teach me the following things:
Every piano player knows the situation that your fingers seem too weak or not stretched enough, that's normal on every skill level.
It's not possible to force rapid performance boosts, especially not by enduring physical pain. Controlled practice with patience is all you can do.
Respect your hands! Yes, you can practice finger strength or range with the right exercises, but if there is any risk in damaging/hurting them, stop.
Never do something that is causing pain. If your hand cannot do the "stretch" you may have to shift. Is the stretch for a chord or a single note run?
I would like to add to this that in general it is a good ideal to stretch before playing as a warm up. But never to the point of pain. We all have to deal wit our individual physical limits. Perhaps in time your body will adjust to get the reach it needs but if it's a far reach then probably not. Pain is different than discomfort. Many players experience a feeling of awkwardness as beginners but eventually get comfortable with the instrument and the demands it places on the body. But pain usually means injury and once you injure tendons, joint cartilage etc. they will scar up and that typically reduces mobility. Stretch gently as a warm up and see how it progresses. Never force you hand beyond its range of motion.
The best advice is, of course, to not cause any further damage to your fingers. The object is to discover what the source of the pain and attempt to alleviate the pain. One definitely does not want to aggravate an injury if it exists. It could be that the pain is caused by developing stronger muscles; that is normal. Pianists are much like athletes in that respect. The pain could also be caused by other factors.
I have a specific example of my own personal pain that was alleviated by better technique. I would get terrible cramps in my left wrist when playing the first movement of Beethoven's Pathetique Piano Sonata. The left hand (my weaker hand) must maintain a tremolo in the bass for most of the movement. The solution was to work on playing without letting my left hand get tense. The tension was the cause of my pain. It was more of a mental fete to keep the left hand relaxed. But, gradually, the pain subsided and I was able to play without pain.
If it truly only hurts slightly, and you're otherwise able to perform the required stretch, then try continuing that way. If the discomfort lessens, that's a good sign; if it grows worse, it's a bad sign: at the very least you need a break from practicing that music, or that passage, and possibly to change what you're doing.
If you're not able to perform the music properly, then your stretch is insufficient. It will not increase, just from trying. It could be that just throwing yourself at the stretch will increase your span by, say, millimeter over time. If you need seven millimeters, that's not nearly enough. (If you're still a child or young adult, not yet fully grown, you have a chance that way.)
It's not advisable to persist in something that hurts, in a situation where the goal is not attainable in that manner.
In the pursuit of a musical instrument, there are some pains along the way, due to the body adjusting to the stresses of acquiring new skills. There are some good pains and there are some bad ones; you have to learn to "play it by ear".
Any sudden, sharp pain is a sign to stop. So is pain that is trending for the worse day over day.
Regarding stretching, do not apply external forces to try to make your reach bigger. If the discomfort you're experiencing is just from your hand's own effort at stretching, that is a lot less dangerous than if you start forcing your fingers into stretched positions using your other hand, or some sort of tool.
