During the acute phase of the COVID-19 pandemic, hospitals faced a challenge to manage patients, especially those with other comorbidities and medical needs, such as cancer patients. Here, we use Process Mining to analyze real-world therapeutic pathways in a cohort of 1182 cancer patients of the Lausanne University Hospital following COVID-19 infection. The algorithm builds trees representing sequences of coarse-grained events such as Home, Hospitalization, Intensive Care and Death. The same trees can also show probability of death or time-to-event statistics in each node. We introduce a new tool, called Differential Process Mining, which enables comparison of two patient strata in each node of the tree, in terms of hits and death rate, together with a statistical significance test. We thus compare management of COVID-19 patients with an active cancer in the first vs. second COVID-19 waves to quantify hospital adaptation to the pandemic. We also compare patients having undergone systemic therapy within 1 year to the rest of the cohort to understand the impact of an active cancer and/or its treatment on COVID-19 outcome. This study demonstrates the value of Process Mining to analyze complex event-based real-world data and generate hypotheses on hospital resource management or on clinical patient care.