The Rishonim explain that hefker is patur from terumos and ma'asros is because terumos and ma'asros are a substitute for the kohanim and levi'im not having an equal share in Eretz Yisrael; where they do have an equal share, e.g. the land is hefker for all, there is no obligation of ter"um.
Produce that grows during a shemita year is exempt from terumos and ma'asros. Had you asked me, I would have said the reason for this din is because everyone has equal access to produce grown during shemita; fields are hefker. However, Rashi (Rosh haShana 15a) writes that the source for this din is from the pasuk, "V'achlu evyonei amcha v'yisram tochal chayas hasadeh," from which the Mechilta darshens that just as an animal eats without having to take ma'aser, so too, when you eat produce during the shemita year you do not have to take ma'aser. According to Rashi the exemption from teru"m during shemita is not based on the usual exemption of hefker but is a special din unique to that year.
One possible approach to understand why Rashi invokes this Mechilta and does not assume shemita falls under the rubric of the usual ptur of hefker is to distinguish between usual hefker, where a person willingly declares his property ownerless, and the special situation of shemita where the halacha forces the owner of produce to surrender his property. The Minchas Chinuch (#84) questions whether shemita produce must be declared or affirmed to he hefker by their owner (afke'usa d'gavra), or whether the produce is automatically in a state of hefker willy-nilly of the owner's will because the Torah decrees it so (afka'usa d'malka). If one assumes the latter to be true, shemita is a unique type of hefker situation that may have its own parameters (see Avi Ezri, Hil. Shemita 4:24).
As we once discussed, the Ketzos understand hefker to be a pledge to not stop anyone who wishes to take possession of one's property; however, until someone actually claims hefker it remains in the original owner's possession (R" Shimon Shkop in Sha'arei Yosher 5:23 strongly disagrees). Given the Ketzos' definition, perhaps the added gezeiras hakasuv is needed by shemita to teach that we are dealing with hefker that makes property truly ownerless even before being claimed.
Another approach taken by Achronim is that unlike hefker, which exempts produce that would otherwise be obligated in teru"m from that obligation (i.e. a ptur), during the shemita year the pasuk teaches us that there is no chiyuv of teru"m to begin with (see Gan Shoshanim #56 citing R' Soloveitchik, Chazal Ish).