The Shulhan Aruch (O.H. 308:31) rules that raw meat is not Muktze because it can be chewed on. Even if the meat is unsalted and may theoretically have blood in it, it is permissible since chewing does not agitate the blood and cause it to become exuded. Furthermore (ibid:32), raw fish is not considered Muktze so long as it is salted. Nowadays, however, it would seem that the reality is the opposite. It is almost unheard of for raw meat to be eaten and especially unsalted meat, since all commercially available kosher meat is pre-salted. Additionally, it is common for people to eat unsalted raw fish such as in sushi.
The Shulhan Aruch (O.H. 308:31) rules that raw meat is not Muktze because it can still be consumed by chewing on it.. Even if the meat is unsalted and may theoretically have blood in it, it is permissible since chewing does not agitate the blood and cause it to become exuded. Furthermore (ibid:32), raw fish is not considered Muktze so long as it is salted. Nowadays, however, it would seem that the reality is the opposite. It is almost unheard of for raw meat to be eaten and especially unsalted meat, since all commercially available kosher meat is pre-salted and as such, the Ben Ish Hai (Shana I Pekude:9) writes that nowadays, raw meat is considered Muktze. In theory, if one set aside steak tartar for consumption, it would be permissible on Shabbat. Additionally, it is common for people to eat unsalted raw fish such as in sushi, and thus, that type of fish would not be considered Muktze.
Interestingly, there is a question among the Moroccan Poskim regarding freezing raw meat on Shabbat. Typically speaking, raw meat should be salted within three days because after that point, the blood found within it dries up and can not longer be removed by salting. As such, after three days, unsalted raw meat should be discarded. Rabbi Machlouf Abuhatzira (Yefe Sha’ah, 56) discusses a scenario in which one has unsalted raw meat which will soon be three days old, and since one cannot salt it on Shabbat, he rules one may freeze it. Rabbi Yedidya Monsonego (Pe’at Yam, 11), quotes Rabbi Haim David Serero, who writes that one could freeze the meat but then went back on his ruling and said it is not permissible as once the blood remains there for three days, even if frozen, it cannot be drawn out as effectively afterwards. Rabbi Shalom Messas (Tevuot Shamesh YD 82) also rules that one may not freeze it. Again, it is uncommon to have access to unsalted meat nowadays, and so this discussion is more academic than germaine.
Summary: Nowadays, most raw meat would be considered Muktze on Shabbat, whereas sushi raw fish would not.