TL;DR: All abortion is banned, except in cases of rape or "where necessary for the preservation of the mother's life" (which allows treatment of conditions such as ectopic pregnancy). The 2018 act permits abortion within the first 15 weeks of pregnancy.
Here is the actual text of the 2007 law:
SECTION 2. (1) As used in this section, the term "abortion" means the use or prescription of any instrument, medicine, drug or any other substance or device to terminate the pregnancy of a woman known to be pregnant with an intention other than to increase the probability of a live birth, to preserve the life or health of the child after live birth or to remove a dead fetus.
(2) No abortion shall be performed or induced in the State of Mississippi, except in the case where necessary for the preservation of the mother's life or where the pregnancy was caused by rape.
(3) For the purposes of this act, rape shall be an exception to the prohibition for an abortion only if a formal charge of rape has been filed with an appropriate law enforcement official.
(4) Any person, except the pregnant woman, who purposefully, knowingly or recklessly performs or attempts to perform or induce an abortion in the State of Mississippi, except in the case where necessary for the preservation of the mother's life or where the pregnancy was caused by rape, upon conviction, shall be punished by imprisonment in the custody of the Department of Corrections for not less than one (1) year nor more than ten (10) years.
[...]
SECTION 4. At such time as the Attorney General of Mississippi determines that the United States Supreme Court has overruled the decision of Roe v. Wade, 410 U.S. 113 (1973), and that as a result, it is reasonably probable that Section 2 of this act would be upheld by the court as constitutional, the Attorney General shall publish his determination of that fact in the administrative bulletin published by the Secretary of State as provided in Section 25-43-2.101, Mississippi Code of 1972.
[...]
SECTION 6. Sections 1, 3, 4 and 5 of this act shall take effect from and after July 1, 2007. Section 2 of this act shall take effect and be in force from and after ten (10) days following the date of publication by the Attorney General of Mississippi in the administrative bulletin published by the Secretary of State as provided in Section 25-43-2.101, Mississippi Code of 1972, that the Attorney General has determined that the United States Supreme Court has overruled the decision of Roe v. Wade, 410 U.S. 113 (1973), and that it is reasonably probable that Section 2 of this act would be upheld by the court as constitutional.
And here is paragraph 8 of the 2018 law:
(8) Construction. Nothing in this section shall be construed as creating or recognizing a right to abortion or as altering generally accepted medical standards. It is not the intention of this section to make lawful an abortion that is otherwise unlawful. An abortion that complies with this section, but violates any other state law, is unlawful. An abortion that complies with another state law, but violates this section is unlawful.
Taken together, it's pretty clear that the 2007 law effectively displaces the 2018 law altogether.