Teenagers are difficult, stroppy and will push the boundaries. This is what they do. It is a natural part of their growing up and stretching their wings. No matter who you are and how good a step parent you are, they will say things to try to hurt you.
The first step is to accept and even expect that this will happen.
In the heat of the moment do not take what they say to heart. This will allow you to separate what they say from your conditioned emotional response.
Later on when things are calmer it will be useful to reflect on what was said. Talk things through with them and work on fixing any underlying problems.
Things do get more complicated when you are a step-parent.
A big part of feeling overwhelmed comes from a feeling of powerlessness.
The child may feel like you are an outsider and not fully respect your authority. (A teenager will rarely respect their real parents authority, let alone a step parents.) Also you may feel like an outsider and that you do not have the authority over the child. The child will sense this and will make the most of it! Kids have an uncanny ability to seek out your weaknesses and exploit them.
It is vital that you discuss this with the real parents. You need to get their agreement as to what the boundaries are for how far you can go in disciplining them. Ideally you should have as much authority as the parents - but this is up to the parents, and is something that develops over time. If you have only been on the scene for a couple of months you will probably not have as much authority as you would after six years.
However, regardless of how much authority you have over the children, you do need the parents support. If you don't have the authority to ground the child for a year, when discussing the problem with the parents it is important that they take the child's bad behaviour seriously and take steps to discipline the children themselves.
The child needs to know that there will be consequences from disrespecting you, either from yourself, or from her parents.
It is worth bearing in mind that a reaction is exactly what the teenager is trying to get. The reason she is coming out with these hurtful things are because she wants you to get mad. She is testing the boundaries, trying to find out how far she can push you. An angry response is considered a win. Respond with calm authority and she will get bored much quicker.