In an Inter-Organizational Business Process (IOBP), independent organizations (collaborators) exchange messages to perform business transactions. With process mining, the collaborators could know what they are actually doing from process execution data and take actions for improving the underlying business process. However, process mining assumes that the knowledge of the entire process is available, something that is difficult to achieve in IOBPs since process execution data generally is not shared among the collaborating entities due to regulations and confidentiality policies (exposure of customers' data or business secrets). Additionally, there is an inherently lack-of-trust problem in IOBP as the collaborators are mutually untrusted and executed IOBP can be subject to dispute on counterfeiting actions. Recently, Blockchain has been suggested for IOBP execution management to mitigate the lack-of-trust problem. Independently, some works have suggested the use of Blockchain to support process mining tasks. In this paper, we study and address the problem of IOBP mining whose management and execution is supported by Blockchain. As contribution, we present an approach that takes advantage of Blockchain capabilities to tackle, at the same time, the lack-of-trust problem (management and execution) and confident execution data collection for process mining (discovery and conformance) of IOBPs. We present a method that (i) ensures the business rules for the correct execution and monitoring of the IOBP by collaborators, (ii) creates the event log, with data cleaning integrated, at the time the IOBP executes, and (iii) produces useful event log in XES and CSV format for the discovery and conformance checking tasks in process mining. By a set of experiments on real IOBPs, we validate our method and evaluate its impact in the resulting discovered models (fitness and precision metrics). Results revealed the effectiveness of our method to cope with both the lack-of-trust problem in IOBPs at the time that contributes to collect the data for process mining. Our method was implemented as a software tool available to the community as open-source code.