Low-calorie and low-fat foods have been introduced to the market to fight the increasing incidence of overweightness and obesity. New approaches and high-quality fat replacers may overcome the poor organoleptic properties of such products. A model of processed cheese spread (PCS) was produced as a full-fat version and with three levels of fat reduction (30%, 50%, and 70%). Fat was replaced by water or by corn dextrin (CD), a dietary fiber. Additionally, in the 50% reduced-fat spreads, fat was replaced by various ratios of CD and lactose (100:0, 75:25, 50:50, 25:75, and 0:100). The effect of each formulation was determined by measuring the textural (firmness, stickiness, and spreadability), rheological (flow behavior and oscillating rheology), tribological, and microstructural (cryo-SEM) properties of the samples, as well as the dynamic aroma release of six aroma compounds typically found in cheese. Winter’s critical gel theory was a good approach to characterizing PCS with less instrumental effort and costs: the gel strength and interaction factors correlated very well with the spreadability and lubrication properties of the spreads. CD and fat exhibited similar interaction capacities with the aroma compounds, resulting in a similar release pattern. Overall, the properties of the sample with 50% fat replaced by CD were most similar to those of the full-fat sample. Thus, CD is a promising fat replacer in PCS and, most likely, in other dairy-based emulsions.