In this paper, a simple and efficient synthetic route for the preparation of new heterocyclic amino acid derivatives containing azetidine and oxetane rings was described. The starting (N-Boc-azetidin-3-ylidene)acetate was obtained from (N-Boc)azetidin-3-one by the DBU-catalysed Horner–Wadsworth–Emmons reaction, followed by aza-Michael addition with NH-heterocycles to yield the target functionalised 3-substituted 3-(acetoxymethyl)azetidines. Methyl 2-(oxetan-3-ylidene)acetate was obtained in a similar manner, which was further treated with various (N-Boc-cycloaminyl)amines to yield the target 3-substituted 3-(acetoxymethyl)oxetane compounds. The synthesis and diversification of novel heterocyclic amino acid derivatives were achieved through the Suzuki–Miyaura cross-coupling from the corresponding brominated pyrazole–azetidine hybrid with boronic acids. The structures of the novel heterocyclic compounds were confirmed via ¹H-, ¹³C-, ¹⁵N-, and ¹⁹F-NMR spectroscopy, as well as HRMS investigations.