Coffee is one of the most widely consumed beverages worldwide. Consequently, many by-products are generated during coffee processing, including the pulp, a source of antioxidant phytochemicals such as phenolic compounds and caffeine, reducing oxidative stress. However, phenolics’ antioxidant properties are physiologically restricted to their bioaccessibility and bioavailability. This study aimed to investigate the gastrointestinal behavior of the coffee pulp’s phenolic compounds under simulated conditions. The coffee pulp, obtained from the Arabica variety by the wet processing method, was milled and subsequently digested following the in vitro INFOGEST method. Phenolic compounds were analyzed using colorimetric and UPLC-MS/MS methods. The in vitro antioxidant capacity was estimated by the ABTS method. The potential bioavailability was predicted using in silico tools. The coffee pulp showed a high content of phenolic acids, especially chlorogenic (1011 ± 28 µg/g), protocatechuic (1757 ± 7 µg/g), and gallic (469 ± 20 µg/g) acids, and flavonoids, particularly quercetin derivatives. The caffeine content (5060 ± 67 µg/g) stood out among all the phenolic compounds, 4.6-fold higher than total chlorogenic acids and 1.4-fold higher than total phenolic compounds. Although the total phenolic content and antioxidant activity significantly increased (p < 0.05) all over the digestive process, the bioaccessibility of the individual phenolic compounds decreased (p < 0.05) throughout the digestive process. Hydroxybenzoic and hydroxycinnamic acids showed high intestinal bioaccessibility (79.0 ± 12.6 and 82.3 ± 11.1%, respectively), while flavonols and flavones exhibited lower values (58.7 ± 8.9 and 41.9 ± 6.8%, respectively). Caffeine (83.1 ± 5.9%) also exhibited high intestinal bioaccessibility. The potential bioavailability, expressed as human intestinal absorption, was highest for caffeine (74.0 ± 5.3%), followed by hydroxybenzoic acids (48.6 ± 7.8%) and hydroxycinnamic acids (22.8 ± 3.1%), and finally, the lowest values were obtained for flavonols (13.6 ± 2.2%) and flavones (7.8 ± 3.1%). Then, although exhibiting similar bioaccessibilities, caffeine may reach the bloodstream and target organs in a higher proportion than phenolic compounds. These results provide new knowledge into the gastrointestinal behavior of antioxidant phenolic compounds and caffeine from the coffee pulp, supporting its use as a new antioxidant food ingredient.