How can you get a period if both fallopian tubes are removed?

Not in the loop. Normal menstruation depends on 1) a funtioning endometrium, 2) an open cervix, and 3) a hormonal sequence (estrogen followed by progestin, then progestin withdrawal) from the ovaries in response to timed hypothalamic/pituitary signals. Thus, a woman needs a working uterus, endometrium, ovaries, and pituitary to have a period. Notice the fallopian tubes are not part of the loop.
Not related. Periods are caused by hormones (which come from the ovary) and the endometrium (that reacts to the hormones and is in the uterus). The tubes are irrelevant to vaginal bleeding.
Menses. Menstrual flow comes from the uterus in which the uterine lining is stimulated by the ovaries. The fallopian tubes have no control over menstrual flow.