He might initially show annoyance. After all, Hermione is often seen as a know - it - all in his eyes. But his sense of justice and his underlying good nature (despite his cold exterior) would kick in. He'd untie her in a rather brusque manner, but then start to question her about how she got into this mess. Depending on her answer, he might offer some cryptic advice on how to avoid similar situations in the future.
Snape might be suspicious at first. He might think it's some sort of trick or part of a bigger plot. However, as he observes Hermione more closely and realizes the genuineness of her situation, his attitude could gradually change to one of reluctant assistance. He might even offer some words of wisdom, albeit in his typical sarcastic way, to help Hermione regain her strength.
She might be initially defensive. Hermione is a proud and independent character. So, when Snape finds out about her arm, she could be worried that he'll use it against her in some way, like taking away house points or using it as an excuse to give her extra work.
He is often very suspicious. He might immediately think it's some kind of trick by the Marauders or their descendants. He'll likely try to figure out how to use it to his advantage against those he dislikes.
Snape might initially be shocked. He's not one to show much emotion openly, but internally he could be very disturbed. He might start investigating what happened to Hermione immediately, using his skills in potions and magic to try and find a cure or at least understand the cause.
He may show a rare moment of kindness. Given his own past traumas and experiences, he might empathize with Hermione on some level. He could offer her some words of wisdom or even some form of magical assistance to help her get better.
He might immediately go into a protective mode. He could use his potions knowledge to quickly make a healing draught for her. After all, Snape is very skilled in potions, and Hermione being hurt would likely trigger his instinct to help.
He might be initially startled. Snape is used to seeing Hermione as a strong - willed and confident student. So seeing her crying could catch him off - guard. But then he might quickly put on his usual cold facade and ask her curtly what's wrong.
He could be secretly worried. Snape might use his knowledge of potions and dark magic to try and find a cure or at least a way to stop the bleeding. He may also be conflicted, as his past relationship with Harry and his loyalty to different sides in the wizarding world play a role in how much he wants to help Harry.
He would probably be in shock. Snape has spent so much time around Harry in one way or another throughout his years at Hogwarts. His immediate reaction could be disbelief. He might stand there frozen for a moment, unable to process what he's seeing. Then, the full weight of the situation would hit him, and he could break down in a rare display of raw emotion.
One possible plot could be that Hermione was set up by some dark wizards who wanted to use her as bait to lure in Harry Potter or other members of the Order of the Phoenix. Snape, being a double agent, stumbles upon her while on one of his secret missions. He might initially be conflicted between his loyalty to the Death Eaters (on the surface) and his true allegiance. He decides to help Hermione, using his knowledge of dark magic to free her from the bindings and then they have to work together to escape the place before the real villains return.