<p>The <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Pi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Π</mi> </math></EquationSource> </InlineEquation>-operator plays an important role in complex analysis, especially in the theory of generalized analytic functions in the sense of Vekua. In this paper, we present a generalized <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\Pi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Π</mi> </math></EquationSource> </InlineEquation>-operator for slice monogenic functions and investigate its mapping properties. Furthermore, a left and right inverse and the adjoint operator of the generalized <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\Pi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Π</mi> </math></EquationSource> </InlineEquation>-operator are given. As an application, we introduce a slice Beltrami equation, which reduces to the classical complex Beltrami equation when the dimension is 2. We provide a norm estimate for the generalized <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\Pi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Π</mi> </math></EquationSource> </InlineEquation>-operator and show how it can be used to establish the existence of solutions to the slice Beltrami equation.</p>