Why do alpha and beta decay produce new elements but gamma decay does not?
Alpha and Beta decay processes produce physical particles. Gamma decay produces gamma rays which are waves and thus no particle change occurs.
Alpha decay and beta decay produce physical masses (consisting of two neutrons and two protons and either an electron or positron, respectively). These physical masses originate from the nucleus of a radioactive isotope and as a result, their emission from a nucleus results in the make-up of the nucleus itself changing. A changed nucleus essentially results in a new element (or isotope) being formed.
Gamma radiation exists in the form of Gamma Rays which exist as waves - not particles or masses. These waves are incredibly high in energy - this is why gamma radiation is considered as being so dangerous to living organisms. The energy is emitted during radioactive decay and although this may result in an overall energy change of a nucleus, it does not necessarily mean the physical make-up (i.e. number of protons and neutrons) of the nucleus changes - and thus the element stays the same.