The reason for shmitta is similar to shabbos and is even called "shabbos" so why do we have it only in Israel? We keep shabbos everywhere. Unlike other mitsvot depending on the 'land' they are for 'growing' things in Israel. Like keeping trumot or kilaim. This mitsva is the opposite, its for not growing. So it shouldnt have anything to do with kedusha of the land.
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The Mishnah in Kiddushin states that most land-dependent mitzvos only apply in Israel. The gemara quotes a beraysa to show that
Halachically, Shabbos applies everywhere since it is חובת הגוף. Shemitah is a shabbos for land, so it just applies in Israel. Hashkafically one can give many different reasons why land-based mitzvos don't apply in chutz l'aretz, e.g:
The Mitzvos of the land are because of the special connection to the land and wouldn't make sense elsewhere. One could also say Mitzvos only apply to something 'holy' (either the person or the land). Outside Israel, the Jews aren't attached to the land enough for the mitzvos to 'kick in'.
(See also the Ramban and Sifri on how the 'true' fulfillment of all mitzvos is in Israel, though I'm not sure it helps answer this question.)