Your mental health can affect your physical health and vice versa, in my opinion it is best not to separate them, but to see it as one intertwined entity, although physical and mental health is often quoted separately, suggesting that they are apart and not the same, in fact, if one is detrimentally affected for whatever reason, the other will also feel the impact of that affect.
For instance, if you have the flue or a bad cold. your usually not going to be in a content or happy state of mind, and if you feel anxious your physical self will show symptoms, maybe your heart rate will rise and your breathing become shallow and faster, in some cases stopping you from doing something or starting a panic attack.
Some kinds of medication can make people anxious or depressed, that is just a physical reaction having an emotional impact, from a side affect of the drug that has been prescribed.
Alcohol, although a physical substance, when it enters into the body and reacts with the physical chemistry of the body, it has a reaction that changes the way people react, it provides both emotional and physical changes that can sometimes become extreme in nature
Another way people can understand the how the mind can affect the physical body is when they become sexually aroused after seeing an attractive sexual photo, or after having a sexually stimulating thought, after all the mind can be a powerful physical stimulus.
A poor mental state of mind can lead to poor life choices, people who are overly stressed often forgo healthy eating, or increase their levels of smoking or drinking, and that will in time have a detrimental affect on the physical self, so yes poor mental health can have a negative impact on the physical body.
Anyone doing more exercise and eating well will find it often has a positive effect on the body, as well as having a possible positive beneficial impact, on the persons mental health, if you improve one you will probably improve both.
Poor mental health can kill, problems such as depression can lead to suicidal thoughts and increase the risk of suicide, and that is a direct threat to the physical self.
So take care of both your mental and physical self, see it as a single harmonious entity with two sides that need equal care and attention and you will be better served by both.