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.
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.
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 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.
She might initially be shocked and scared. But then she would start to think rationally and try to find a way to outwit Snape. For example, she could start to gather evidence against Snape's own wrongdoings, if there are any, so that she can turn the tables on him.
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.
Snape would probably be quite surprised at first. Hermione is known for her academic prowess and self - sufficiency. His reaction could range from being dismissive, thinking she should be able to solve her own problems, to being intrigued by the nature of her request. If it's something related to the dark arts or a mystery in the wizarding world, his interest might be piqued, but he'd still be guarded in his response. He might even try to use her request as a way to gain some advantage or information for himself.
He could also be a bit sarcastic in his response. Snape has a sharp tongue, so he might say something like 'Miss Granger, what makes you think I have the time or inclination to help you?' But as Hermione explains her situation, he might gradually soften, realizing the seriousness of the matter. Maybe he starts to see a bit of himself in Hermione's thirst for knowledge.
Hermione may also start to scheme. She'll use her intelligence to come up with a plan. For instance, she might start to collect evidence against Snape, something that she could use to counter his blackmail. She'll research old school rules or find out secrets about Snape that she can hold over his head instead.