Yes, it's one of regular ways to form an adjective. Usually its -ский -ская -ское - ские (уругвайский, бразильский: belonging to/related to Uruguay/Brazil), but for Слуцк (a town) it is "cлуцкий'. You'll find this adjective in the corresponding article of Russian wikipedia. When a name ends with -цк or -ск, we add -ий without additional -ск-. It's quite natural given the fact, that -цк (<-ть+скъ, -чь+скъ etc.) and -ск is an ancient adjective suffix itself, moreover - the same suffix as in -ский:) -ский is also common ending for russian trnscription of Polish surnames (-ski in Polish). People with Russian surnames ending with -ский often have Polish, Jewish, or Polish-Jewish ancestry (due to the ways of Jewish migration), but not necessary. Suffix is common to all East Slavic languages and Polish, but the history of getting surnames is differnt for different regions and peoples. Note that some portions of Belarus, Ukraine and Lithuania belonged to Poland pretty recently, while even greater territory was controlled by Polish-Lithuanian state some 400 years ago. Surnames ending with -цкий are pretty rare. --- Sorry if the answer is too long:) I want to sleep and I always write long stories when i'm half asleep)

Yes, it can be adjective in example "Слуцкий кот" кот из Слуцка.