Multi-antenna (or MIMO) processing is a promising solution to the problem of jammer mitigation. Existing methods mitigate the jammer based on an estimate of its spatial signature that is acquired through a dedicated training phase. This strategy has two main drawbacks: (i) it reduces the communication rate since no data can be transmitted during the training phase and (ii) it can be evaded by smart or multi-antenna jammers that do not transmit during the training phase or that dynamically change their subspace through time-varying beamforming. To address these drawbacks, we propose Joint jammer Mitigation and data Detection (JMD), a novel paradigm for MIMO jammer mitigation. The core idea of JMD is to estimate and remove the jammer interference subspace jointly with detecting the legitimate transmit data over multiple time slots. Doing so removes the need for a dedicated and rate-reducing training period while being able to mitigate smart and dynamic multi-antenna jammers. We provide two JMD-type algorithms, SANDMAN and MAED, that differ in the way they estimate the channels of the legitimate transmitters and achieve different complexity-performance tradeoffs. Extensive simulations demonstrate the efficacy of JMD for jammer mitigation.