I completely agree with the previous answer from Notstingy. However, I'd like to provide you with a more detailed explanation.
Now, a mini PC is like a tiny powerhouse that can do a lot, when it comes to holding a graphics card, it's a bit like trying to fit a massive turbo engine into a tiny sports car. Sure, it would be awesome to have that extra power, but most mini PCs are not designed with a lot of extra space inside. They're more focused on being compact and portable.
Some mini PCs, however, do come with slots where you can plug in a graphics card, just like a regular desktop. But here's the thing: those mini PCs are not as common as the ones without those slots. So, if you already have a mini PC or you're thinking of getting one, you need to check its specific model and specifications to see if it has that magic slot.
If your mini PC doesn't have that slot, don't despair! Many mini PCs are built with integrated graphics, which means they have a built-in graphics chip on the motherboard. It's like having a decent graphics card already included, just not an extra powerful one you can upgrade later.
So, while some mini PCs can indeed hold a graphics card, it's not a universal feature. Make sure to double-check the specifications of your mini PC to know for sure if you can add that extra graphics oomph or if you'll be rocking with the integrated graphics it comes with.
I hope that mini PCs will someday be able to use discrete graphics cards, but I always thought this was more an issue of power consumption. If a PC has a full power supply of at least 650W, then mini PCs are devoid of such things. The story about dimensions is also relevant, but I think this is also a solvable issue, theoretically you can make small discrete graphics cards.