/u/freedmenspatrol addresses the banning of the slave trade in the CSA Constitution here, which I think will hopefully help to explain the interplay of those two clauses.

The first provision is a ban on importing slaves to the Confederacy from abroad, which is discussed in the post /u/Georgy_K_Zhukov linked. That leaves us the second one.

Bills of attainder and ex post facto laws are prohibited in the United States Constitution and the language here essentially carries that over. The new one is an absolute constitutional prohibition on restricting slavery. That was the great fear that the white South had of antislavery men taking over the federal government. Direct abolition was possible, but probably not in the near term. Rather the Republicans might pass laws that reduce the power of enslavers over the people they enslave or restrict the spread of slavery. The GOP literally ran on the latter platform.

The Confederates knew that they were seceding to form a slaveholding republic to replace the last one, which had ceased to be slaveholding enough for many of them. The last thing they wanted to do was only leave the system radically tilted in their favor and be in the same position come another fourscore and seven years. By dropping it into their constitution, they were resolving the ambiguities and silences in the US Constitution that had allowed antislavery politics to become a realistic possibility rather than the preserve of a nutty fringe.

One of the biggest ambiguities here is that the US Constitution does not explicitly recognize a right to what they called "property in man" but does protect a general right to property. Is a person property? We, the People doesn't say that one is or isn't covered. Proslavery thinkers insisted that it was and so they should be able to get, say, judgments against people who "stole" their slaves via the federal courts.

Antislavery thinkers in turn point out that the Constitution doesn't say what it doesn't say. Where it does mention slavery it directly avoids granting property rights over a person in as many words, instead talking around what everyone understands to be enslaved people by referring to, for example, the rendition of fugitive slaves across state lines. Fugitive slaves are people who owe service, with the right being granted to the service, rather than the person.

This is, to be blunt, a fig leaf. The men in Philadelphia were not deluded or in denial. They understood from the get-go that this was about enslaved people but a few of them had squeamishness about putting the word "slavery" into their document for posterity. Their squeamishness, without any real intention on their part, opened the door for antislavery men in the subsequent generations to develop a reasonable-sounding, if historically absurd, theory that the US Constitution was an innately antislavery document and use that theory to good effect. By wrapping themselves in the Constitution and expressing the vague unease that many northern whites have with slavery, they make antislavery a marginally acceptable thing to have in the body politic.

Antislavery is rarely popular and antislavery speakers are still subject to extralegal violence well into the nineteenth century even in places like Boston. Most white Yankees are fine with slavery as long as it stays far away. They think of it a bit like we might think of injustices in distant countries; it's very bad and someone should do something, but it's far away and what's it to do with us? National controversies over slavery always move more northern whites toward antislavery, but so long as they're infrequent and managed with some kind of "compromise" whites tend to get over it. When they cease to be so infrequent and the resultant non-compromises become more intrusive and more obviously unjust to white people right at home, things change and antislavery constitutionalism helps situate the movement within the mainstream of northern reformist thought. So as those usually disinterested or indifferent Yankees feel more pushed, what we could call movement antislavery or the antislavery party (ultimately the GOP, but they have important precursors in the Liberty and Free Soil parties) is a more natural home and easier to transition into.

The Confederates watched all that with growing horror. Knowing the score and with none of the Revoutionary-era squeamishness, they went right to the heart of things. They were in the main not temporizers who would agree in theory that slavery was bad, but regret that they had no smooth way to get rid of it. By 1860, the majority are willing to say aloud what they and their grandparents probably believed two generations further back: slavery is good, the bedrock of their civilization, and its one indispensable institution. Therefore it deserves protection as the cornerstone of their liberties, analogous to how modern Americans sometimes view the First Amendment. Hence Article 1, section 9.4.