I don’t understand Japanese so I only know the story based on the English subtitles. Is there a reason given to explain why Ashitaka couldn’t have cut off his arm to stop the curse spreading?
There is no explicit statement in the Japanese script of why he could not cut off his arm, but there are two fairly obvious reasons why it seems like it would be a terrible idea.
Amputating an arm is likely to kill you. Losing a limb opens you up to shock, blood loss, and gangrene. Without modern sterilization techniques, such a wound would be almost certainly fatal, even if the bleeding could be stopped. (Even the pain could be enough to kill some patients, although I suspect Ashitaka is tougher than that.) Stanching the bleeding with a tourniquet would be easier if the limb were amputated lower down, near the elbow, than if it were cut off close to the shoulder. However, it is not clear that removing only the lower arm would be sufficient; and that brings us to the second major reason not to just amputate.
It is not clear that removing the arm would even work. Ashitaka's arm has been infected with a magical curse. Clearly, the focus of the enchantment/infection is on his forearm, but without knowing a great deal more about the nature of the curse, it would not be possible to say that cutting off the obviously damaged part of the limb would be sufficient to eliminate the curse entirely. If might have extended, less visibly, all through Ashitaka's body; that would probably mean that amputation would slow the advance of the enchantment but not stop it.
Given these facts, trying to learn more about the nature of the curse is a very logical approach to take. From Ashitaka's viewpoint, it might ultimately turn out that amputating the cursed limb would be the correct action to take. However, the curse is not spreading too quickly, so he can afford to take his time before making a precipitate decision. And maybe he knows that if he does not find out anything useful about the curse in a reasonable amount of time, he will need to get his arm hacked off.
Maybe Ashitaka considered cutting off his arm but discounted it due to the practical difficulties of cleanly cutting off one of his arms with a sword stroke by the other arm.
If the infected arm was his sword arm it might not be possible for him to cut off the arm of another person, even a prisoner held tight with his arm in position for the stroke, with the arm that wasn't his sword arm. And it would probably be even harder to use the non sword arm to slice off his sword arm in one clean stroke - instead of hacking and hacking and hacking - especially if he had to cut if off high up toward the shoulder and thus close to his torso.
If someone cut off Ashitaka's arm, and two men held the two ends of the arm in front of Ashitaka, it would have been easy for Ashitaka - if he still had his sword arm - to cut the already detached arm in half. But it would not have been so easy with the awkward angles necessary with the arm still attached to him. And it would also be hard if the sword arm was the infected arm and he had to use his non sword arm.
And then it would be necessary for one-armed Ashitaka to put a tourniquet and/or bandages on the stump of the arm, single handed.
So if Ashitaka decided to amputate his arm, he would probably need to get someone else, preferable an executioner, and/or a doctor, and some nurses, to do it, explaining that he had a magical curse in his arm.
But that would be defined as "have someone amputate his arm", not "cut off his arm". It would not be the same action as the question asks about.
So it would be highly unlikely that Ashitaka would cut off his own arm to stop the curse, as the question asked. And if Ashitaka was desperate and decided on amputation, he would probably have to have someone else do it, which would be a different course of action.