You have asked complicated questions. With regard to it being normal to feel depressed or exhausted when going to therapy, the answer is that it depends. Generally, I do think that feeling exhausted is normal. It takes time, energy, and devotion to decide to see a therapist and really work on your issues. Therapy can be emotionally draining. This may be especially true for you because you mentioned that it took you some time to decide to keep your initial therapy appointment. Clearly you struggled with this decision. What is important and encouraging is that you did keep the appointment. It shows that you recognize that you need support and guidance.
With respect to feeling depressed about going to therapy, I am unclear about why you are feeling this way. People generally feel depressed and then subsequently seek therapy. If I understand you correctly, you are feeling depressed about going. Some people mistakenly feel weak for going to therapy thinking that they “should” be able to fix things on their own. The more likely explanation is that you are struggling with therapy because it may mean an end to your marriage. Taking action to end your marriage may cause you to feel guilty and be a major source of anxiety. The prospect of ending a marriage is a monumental life change and is an extremely difficult decision. It is possible that your feelings of guilt are contributing to your depression.
The cutting may be your reaction to you deciding to engage in therapy and possibly end your marriage. Cutting is a form of self-punishment and is an inappropriate and misguided coping mechanism. If you are feeling guilt over the idea of ending the marriage then cutting may be your way of enduring the guilt. The cutting probably makes you feel better because you think that you are “paying for” whatever mistakes you believe that you have made, now or in the past, and this comforts you.
It is also believed that cutting is a form of self-control in that you decide how many cuts, how often, and how deep. What you must recognize is that the feeling you get from cutting is an illusion. The truth is that cutting is not only dangerous but it is a sign that your life is out of control. It may make you feel good temporarily but it is extremely and quite literally self-destructive. It is unhealthy for you to be abusive toward yourself. You mentioned that you were abused as a child. You endured abuse as a child and now are inflicting it upon yourself willingly. I hope that you come to realize that you have taken enough abuse.
I do not know if you should stay in therapy with your current therapist. It is clear that you could benefit from therapy but I am not sure if you have found good help. Have you talked to your therapist about the cutting? If you have not then you should. If you are not able to talk to your therapist about your cutting then you should find another therapist that you can open up to. It is normal for therapy to be difficult and exhausting but it is not normal for you to, after a difficult session, take to cutting yourself. I hope this provides you with some clarification. If you have further questions, please do not hesitate to write again. If you would, please consider writing in again to let me know how you are doing. I wish you luck.