Background: A validated, standardized, and feasible test to assess muscle power in older adults has recently been reported: the sit-to-stand (STS) muscle power test. This investigation aimed to assess the relationship between relative STS power and age and to provide normative data, cut-off points, and minimal clinically important differences (MCID) for STS power measures in older women and men. Methods: A total of 9320 older adults (6161 women and 3159 men) aged 60–103 years and 586 young and middle-aged adults (318 women and 268 men) aged 20–60 years were included in this cross-sectional study. Relative (normalized to body mass), allometric (normalized to height squared), and specific (normalized to legs muscle mass) muscle power values were assessed by the 30 s STS power test. Body composition was evaluated by dual energy X-ray absorptiometry and bioelectrical impedance analysis, and legs skeletal muscle index (SMI; normalized to height squared) was calculated. Habitual and maximal gait speed, timed up-and-go test, and 6 min walking distance were collected as physical performance measures, and participants were classified into two groups: well-functioning and mobility-limited older adults. Results: Relative STS power was found to decrease between 30–50 years (−0.05 W·kg⁻¹·year⁻¹; P > 0.05), 50–80 years (−0.10 to −0.13 W·kg⁻¹·year⁻¹; P < 0.001), and above 80 years (−0.07 to −0.08 W·kg⁻¹·year⁻¹; P < 0.001). A total of 1129 older women (18%) and 510 older men (16%) presented mobility limitations. Mobility-limited older adults were older and exhibited lower relative, allometric, and specific power; higher body mass index (BMI) and legs SMI (both only in women); and lower legs SMI (only in men) than their well-functioning counterparts (all P < 0.05). Normative data and cut-off points for relative, allometric, and specific STS power and for BMI and legs SMI were reported. Low relative STS power occurred below 2.1 W·kg⁻¹ in women (area under the curve, AUC, [95% confidence interval, CI] = 0.85 [0.84–0.87]) and below 2.6 W·kg⁻¹ in men (AUC [95% CI] = 0.89 [0.87–0.91]). The age-adjusted odds ratios [95% CI] for mobility limitations in older women and men with low relative STS power were 10.6 [9.0–12.6] and 14.1 [10.9–18.2], respectively. MCID values for relative STS power were 0.33 W·kg⁻¹ in women and 0.42 W·kg⁻¹ in men. Conclusions: Relative STS power decreased significantly after the age of 50 years and was negatively and strongly associated with mobility limitations. Our study provides normative data, functionally relevant cut-off points, and MCID values for STS power for their use in daily clinical practice.