White-light observations of the solar corona show that there are two characteristic types of Coronal Mass Ejections (CMEs) in terms of speed-height profiles: so-called fast CMEs that attain high speeds low in the corona and slow CMEs that gradually accelerate from low initial speeds. Low and Zhang (2002) have recently proposed that fast and slow CMEs result from initial states with magnetic configurations characterized by normal prominences (NPs) and inverse prominences (IPs), respectively. To test their theory, we employed a two-dimensional, time-dependent, resistive magnetohydrodynamic code to simulate the expulsion of CMEs in these two different prominence environments. Our numerical simulations demonstrate that (i) a CME-like expulsion is more readily produced in an NP than in an IP environment, and, (ii) a CME originating from an NP environment tends to have a higher speed early in the event than one originating from an IP environment. Magnetic reconnection plays distinct roles in the two different field topologies of these two environments to produce their characteristic CME speed-height profiles. Our numerical simulations support the proposal of Low and Zhang (2002) although the reconnection development for the NP associated CME is different from the one sketched in their theory. Observational implications of our simulations are discussed.