Senescent cells are growth-arrested cells that cause inflammation and play a causal role in aging. They accumulate with age, and preventing this accumulation delays age-related diseases. However, the mechanism for senescent cell accumulation is not fully understood. Accumulation can result from increasing production or decreasing removal of senescent cells with age, or both. To distinguish between these possibilities, we analyze data from parabiosis, the surgical conjoining of two mice so that they share circulation. Parabiosis between a young and old mouse, called heterochronic parabiosis, reduces senescent cell levels in the old mouse, while raising senescent cell levels in the young mouse. We show that parabiosis data can reject mechanisms for senescent cell accumulation in which only production rises with age or only removal decreases with age; both must vary with age. Since removal drops with age, senescent cell half-life rises with age. This matches a recent model for senescent cell accumulation developed from independent data on senescent cell dynamics, called the SR model, in which production rises linearly with age and senescent cells inhibit their own removal. The SR model further explains the timescales and mechanism of rejuvenation in parabiosis, based on transfer of spare removal capacity from the young mouse to the old. The present quantitative understanding can help design optimal treatments that remove senescent cells, by matching the time between treatments to the time it takes senescent cells to re-accumulate.