X-rays can cause mutations in human DNA and might lead to cancer.
Sad but true.
It all depends on many factors. In fact too many.
X-rays are weakly absorbed by the human body. The part that is not absorbed has no effect.
Most important mode of absorption is ionization. Lots of ions (ion-pairs) are produced along the path and most of them promptly recombine (and become harmless) and a part of these ions can make some damage.
Within a cell, DNA takes up a small volume. But a cell that falls in the path of ionization of the x-ray most likely dies.
It is also possible that the x-ray hits the DNA and causes mutation but the cell lives. If the cell is not rapidly dividing, the damage to the DNA has no effect.
Most of the time, mutations in some random parts have little biological effect.
Most of the cells are not rapidly dividing but there are exceptions. For example, cells responsible for reproduction (testis and ovary) or mammary glands and stuff like that.
If the x-ray photon hits your gonads, and causes a mutation in some important part of the DNA and you are young and active, you be worried.
Also the energy of the x-ray matters: it determines the degree of ionization along its path within the cell (per unit length).
Summary: do not worry but be careful.