The Catholic Health Association of the United States (CHA) is a voluntary association of Catholic hospitals. In 2014, Ron Hamel, the senior ethicist for the CHA, published an article on their website which deals with this question among others. His conclusion is this:
Treatment of ectopic pregnancy can take three forms — expectant management, surgical, and medical....
Expectant management, consists in simply monitoring the situation to see if the tubal pregnancy resolves on its own. Most women are not candidates for expectant management. Surgical treatment can take two forms. One consists in the partial or complete removal of the fallopian tube, which also contains an embryo (salpingectomy). The other involves slitting the fallopian tube and "stopping the destructive activity of the trophoblast by removing the invasive trophoblastic cells along with the damaged tubal tissue." The embryo is also necessarily removed in the process (salpingostomy). The third form of treatment, medical, consists in the administration of the drug methotrexate which prevents the trophoblastic cells from continuing to divide and doing damage to the tube that could result in severe hemorrhaging. The embryo also eventually dies.
(quote from Albert S. Moraczewski, OP, "Ectopic Pregnancy: B. Arguments in Favor of Salpingostomy and Methotrexate," in Edward J. Furton et. al., eds., Catholic Health Care Ethics: A Manual for Practitioners.)
Dr. Hamel comments that "virtually all theologians agree that "salpingectomy constitutes an indirect abortion and so is morally licit. The demise of the embryo is foreseen, but not intended." In other words, the primary purpose of the operation is to save the life of the mother, although as this happens, the embryo must die. It is not directly killed. The other two possibilities, he says, are more ambiguous.
Among Catholic theologians and ethicists, there is disagreement regarding [salpingostomy and administration of methotrexate]. Some see them as a direct attack on the embryo and, so, a direct abortion, while others see them as aimed at removing pathological tissue — the trophoblast — which unavoidably results in the death of the embryo. They judge this to be an indirect abortion.
Dr. Hamel comments
The magisterium has not resolved this controversy. Hence, neither Church teaching nor the ERDs [ethical religious directives, which given what Catholic hospitals may do in order to call themselves Catholic] forbid [these two approaches] (so long as these approaches can legitimately be argued as not constituting direct abortions). ... Given the ongoing debate, it is permissible for Catholic hospitals to employ both salpingostomy and methotrexate.