One of the common criticisms of progressive taxation is that it reduces savings and investment which are essential for growth. That was the rationalization that the Reagan Administration used to make the the federal tax system less progressive. Economists on the left argue that progressive taxation fosters the development of human capital which is pro-growth.
The IMF did some research on this question which is summarized in this article. The data provides some evidence that progressive taxation is associated with economic growth. The data are dependent upon cross national analysis of economic growth in countries with varying levels of tax progressiveness. It is hard to separate out other factors in addition to tax policy that might affect economic growth. On the other hand, the data do not support the claim that progressive tax policies and income redistribution impede economic growth.