What are the psych effects of having a mastectomy?

Tough question. The answer is more complex than can be discussed in this brief space. Suffice to say mastectomy poses a massive challenge to one's psychological balance. The effects depend on the individual, of course, and some women will get to an even better place in terms of mental health. Family love & support, personal strategies for positive mindset, and professional help are all warranted.
Most difficult issue. For women, this may be the most important and difficult issue to contend with beside the implications of a diagnosis of cancer. Having treated hundreds of unfortunate women with a breast cancer diagnosis over the last 25 years, i can emphatically state that I am amazed at the resilience, strength and heart of my patients to undergo the procedure and then the different stages of reconstruction.
Varies. Women say that losing a breast (or both) affects how they feel about themselves as a woman and a person. For some, this feeling is very intense, for others less so. It can be profoundly influenced by the people we love and how they react. Fortunately, there are many wise and wonderful support groups you may access on line. In the end, we all lose everything: so perhaps we are not just our bodies.