Carbon fiber-reinforced composites are popular due to their high strength and light weight; thus, the structures demonstrate high performance and specific strength. However, these composites are susceptible to impact damage. The objective of this research was to study the behavior of carbon fiber-reinforced laminates based on a polyetheretherketone (PEEK) matrix with six stacking sequences under static and impact loading. Four-point bending, short-beam bending, drop weight impact, and compression after impact tests were carried out. The results were complemented with digital shearography to estimate the damaged areas. Finite element modeling served to assess the failure mechanisms, such as fiber and matrix failure, in different layers due to tension of compression. Three behavior pattern of layups under drop-weight impact were found: (i)—energy redistribution due to mostly linear behavior (like a trampoline) and thus lower kinetic energy absorption for damage initiation, (ii)—moderate absorption of energy with initiation and propagation of concentrated damage with depressed redistribution of energy in the material, (iii)—moderate energy absorption with good redistribution due to initiation of small, dispersed damage. The results can be used to predict the mechanical behavior of composites with different stacking sequences in materials for proper structural design.