I use a small cutter made for max 14 gauge wires, but I'm bad at removing insulation, it takes me a bit of time to get it right, so I end up cutting and repeating, because I see scratches on copper wire were I cut the insulation. Should I ignore it? How bad are these scratches or marks? These are power works behind sockets.
Minor superficial marking is just that. Unimportant. Deep nicks around the circumference create weaknesses. Those would cause problems. Redo.
With the right tools, careful use and a little practice, you will be able to strip insulation without nicking or scratching the copper.
Obligatory X answer: If you have to ask if the nick is bad enough, it's bad enough.
It's not you. It's the piece of junk wire stripper. There are a LOT of really terrible wire strippers out there, either in the $5 tool bin, or they come with variety packs of crimp terminals.
If you only have occasional work to do, take WGroleau's advice and roll an exacto knife around the edge of the wire, pressing just barely enough to penetrate the insulation, not nick the wire appreciably.
Otherwise, go out and buy a really good one. We're talking $12-15. Irwin is the lowest quality I would consider, and not their bottom-end unit either.
It should have a mystery hole about 1/4" from the edge of a side. Bolt shears are nice but not necessary. Having a terminal crimper is usually the mark of a junky cheapie, though it's perfectly possible for a fine tool to have it.
I know it's easy to sit here and spend your money. Rest assured I don't do it lightly. You'll thank me...
Since it isn't clearly specified what the wire will be used for, i will enumerate a few scenarios when copper wires are used, and analyse the impact of the scratches in each case.
a) carry electricity (for the purpose of powering an electrical device)
b) carry electrical signal (which is the same as carrying electricity, but this time, either the intensity/voltage/frequency of the current vary in time, as to encode some digital/analogue signal)
c) generate magnetic field
d) generate heat
e) generate light
Analysis of the impact:
a) as long as there is physical contact between the wire and the next metal part in the circuit, electricity will flow. Scratches do not affect conductivity (this aspect has been previously mentioned in Jeffrey Boettger's answer). The fact that the current will flow is not even influenced by the contact surface between the two metal parts - so scratches don't have the least influence
c) this is the case when the wire is used to make a coil, which is a component widely used in electronics (load speakers are just an example where we use coils). This time, scratches will affect the magnetic field, making in irregular. If the coil has many turns, scratches over a short segment might not be critical, but, from a theoretical point of view, every geometrical irregularity of the wire will affect the magnetic field.
b) this is the case when the wire is used for internet/television/telephone. As i mentioned above, the signal is encoded as variations in the current's voltage/intensity/frequency. None are influenced by scratches in the wire. However, in telecommunications, it is often the case that a pair of cables are twisted together, for the purpose of cancelling each other's magnetic field. That's because magnetic field represents an interference that affects the signal. As i stated at point c) above, if the wire has any irregularities, its magnetic field will not be uniform, meaning that it can affect the neighboring wire's signal.
d) this is the case when the wire is used in electrical heaters. The heat property is only influenced by the current intensity. Scratches will not affect that
e) this is the case when the wire is used for a light bulb. Light, just the same as heat, is only influenced by the current's intensity
Considering the photo provided in the question, i am aware this wire will not be used for either heating or lighting. I just thought it was worth mentioning points d)and e) along with the other points.
There is also a mechanical aspect involved - how resistant will be the wire to repeated bending. Scratches can be of two types: longitudinal (along the wire) or transverse (across the wire). Bending has the potential to enlarge transverse scratches, but it will not influence longitudinal scratches. (This aspect has also been mentioned in a comment by Hot Licks).
Small scratches should not affect conductivity of the copper wire at all. This is common when stripping wires bare with knives, side cutters and other misc tools. When one is preparing copper wire they should get into the habit of using wire strippersthis particular tool strips wire to gauge minimizing damage.
Don't be to worried about little nicks and scratches. Just be mindful of the plastic coating. Exposed wire could be a potential shock or fire hazard.
Like @RedGrittyBrick already mentioned, if it's superficial surface markings, then no worries, they're only markings. Use a flashlight and magnifying glass, so you can try see to see if you would call them surface markings vs. a real nick. If you see something you'd call a "nick", then just redo the stripping.
I only occasionally do electrical work, but have broken wires at the insulation just by moving them slightly in the box. Since it's after the fact, I can only guess it was due to nicks. And if so, no way to measure how deep the nick was before the break. So better safe than sorry.
Also like @Harper says, make sure you have good wire strippers. Try about a dozen times on some extra wire, if you are not getting the hang of it, then maybe you should consider the tool then. If it's the red cutter tool with screw, make sure that the screw has been set properly for 14 gauge. If it's the yellow tool with multiple positions, then make sure a) you're actually doing 14 gauge wire and b) the wire is going into the 14 gauge position and not its 16 gauge neighbor. It is possible to strip with the 16 gauge position but will usually lead to bad results.