so, it's entirely dependent on how deep you're actually cutting (sorry for the colloquial terms) but is it:
skin (bleeds a lot for a second, stops quickly)
if this is the case, clean it with an antiseptic, neosporin if you're the type, and a bandaid, and it should completely dissapear.
styro (takes a few seconds, sometimes almost a minute to start bleeding, when cleaned you can see subcutaneous fat underneath (which looks like styrofoam, hence the name))
this is when things usually start leaving scars, doesn't need stitches (not sure if surgeons would do it usually), but it's imperative to sanitize, antimicrobial/antibacterial, and keep covered. repeat daily, until healed.
full fat tissue (cuts are usually wider depending on length, but usually 3-4 as wide as it's predecessor, usually bleeds a slowly for a long while, can see yellow/off white fat bubbles underneath),
this is where most suggest getting stitches. it is possible to take care of at home, but no matter the amount of care, it will most likely scar at least a little. recomend the same as styro, HOWEVER, butterfly bandages are your friend here, apply them underneath you cover bandage as tightly as you can, and change everything out 2-3 times a day, more often if it bleeds excessively or bandages become loose. to help stop initial bleeding to apply bandages, elevate the wound at least 1ft above heart level, and apply HEAVY pressure with a clean and sterile rag. it's gonna hurt like fuck, be warned, usually huets more than getting the wound itself (depending on area). if you are unable to stop the bleeding, you should go to the hospital.
(there are fucked up methods involving superglue, or dental floss (unflavored) and a sewing needle, but they require some practice to get right, and will definitely scar badly.)
finally full muscle (cuts are very wide, sometimes as wide as long, completely a toss up whether it soaks everything in blood or doesn't bleed at all, can see red and pink ligaments underneath).
this is a hospital only case unfortunately. it's highly possible nerve damage, internal bleeding, or permanent muscle tissue damage has occured. no home remedy will fully fix this.
if stranded, and unable to get to a hospital quickly, it's recommended to tie a double tourniquet above the injury, and it WILL feel like you're gonna die if done correctly (you won't, unless you leave it there for hours, in which case, your leg may start to develop minor necrosis, nerve damage, burst cappilaries, or clots)
ONLY in horrible, "i can't get to the hospital for days because i'm lost in the amazon rainforest" type situations, there are medical kits that you can get after a short class that contain specialiazed wound glue, stitching tools, antibiotics, and a few other emergency tools, however, they usually keep a log of how often you pick them up, but idk if they say anything tbh
[source: when i lived up in alaska, all of us in upper management of the restaurant had to do the class, learn field wound dressing, and learn how to be really fucking bad at stitching lol]