Two young Vrishni brothers Sankarshana Balraam and Krishna, who happen to be nephews of Kamsa (Mathura's king) led a coup and assassinated the reigning king of Mathura. Krishna sends the two wives of Kamsa (who happened to be daughters of Jarasandha of Magadh) back to Girivraja (modern Rajgir) and this open defiance of Mathura created a vacuum in North-Central India. The proxy king Ugrasena who was established by Vrishni yadava brothers took a neutral stance (rather less pro-magadh stance) as opposed to the "satellite state of Magadh" which Mathura was under Kamsa. This gave an opportunity to Magadh to intercede in the politics of Saraswati basin and directly enter into competition with Kurus. Magadh was aware of the fall-out in Panchal-Kuru tango.
According to Srimad Bhagvat, Jarasandha raided Mathura 17 times. Vrishni brothers and other Yadavas managed to fend off these raids. However, on 18th occassion, Magadh enticed a Mlechha king from west to invade Mathura from west, while Magadh invaded from east to finish off Yadava-Influence from Mathura. Mostly this was some Persian king who was "probably" in this game to earn a quick buck. I don't think it was realistic on part of Kaal-Yavan to think that he would be able to establish a stable polity in India with Kuru and Magadh around in neighbourhood.
The Vrishni brothers managed to trick Kaal-yavan and slyly assassinated him. Krishna is described to be the chief architect of this assassination for which he is popularly castigated as "Ranchhod das" (one who flees from raging battle). Vrishni brothers travel southwards while Magadh army pursues them. They travel through the realms of their Yadava Brethren which were spread all over Central India and Upper Deccan plateau. The Vrishni brothers manage to defeat and kill Jarasandha's ally "Shrugaal" of Kolhapur and enter the province of Gomantaka (Modern Goa and Konkan). While hiding in forests and hills of Sahyadri mountain ranges, Magadh army manages to trace them and lays siege to the hill-fort they are hiding. However, since they lack any siege weapons, Magadh army started advance towards citadel of hill-fort in order to capture OR kill the Vrishni brothers.
The brothers managed to escape the siege somehow and started a forest fire, which engulfed the besieging Magadhan army and broke their formations. Jarasandha returns to Magadh after this fiasco. The Vrishni brothers meet Parashurama in Dakshinapatha forests and according to Harivamsha, it is here where Krishna receives "Sudarshan Chakra". All this part is missing in MBH, but present in Bhagvatam and Harivamsha.
Meanwhile, Magadh's strategy did not prove futile. While Jarasandha could not finish off the Vrishni brothers in his Deccan escapade, he managed to dislodge Yadavas from Mathura and forced them to migrate to the extreme periphery of India - Saurashtra and Dwarika situated at the mouth of Saraswati River basin. While otherwise, this would have been a prime location just like Sindh, but living at the mouth of a drying river isn't very wise thing, in long run. The clan of Vrishnis settle in Saurashtra in artificially created city of Dwarika, while maintaining a nominal presence in Mathura.
The Shoorsena Yadavas of mathura thereafter dwindled both in numbers and significance. Perhaps, Jarasandha decided to let Shoorsena Yadavas die naturally instead of asking for curses from mango abduls living there and who were pissed off by constant raiding and warfare by Magadh. Yadavas seem to be spread across Central Indian region and Deccan plateau and western Ghats. I can't help comparing the expanse of Yadavas with expanse of Marathas. Various houses of Yadavas (like marathas) ruled western Maharashtra, Vidarbha and Madhya-Pradesh (and later Gujarat). While Magadh was friendly with all them, Jarasandha was bitter enemy of Vrishni Yadavas of Mathura. After dislodging Vrishnis from Mathura, he let Shoorsena Yadavas be. I think Magadh did not want the powers of South-Central India to enter as participants in power-struggle of Indo-Gangetic plains. The Vrishnis of Mathura were precisely trying to do that.
One thing that we need to keep in mind, is that, in Indian system of polity, there aren't any "inviolable boundaries" of "nation-states". Although all these Mahajanapadas were individual and sovereign political units who were recognized by intellectuals, traders and other peers, they weren't anything like modern "Nation-states". Hence many times conquests in form of "ashwamedha Yagna" and "Raajsooya-Yagna" did not involve the practice of finishing off the defeated dynasty and annexation of the province which was won. This system was unknown to India until advent of Nanda-Dynasty of Magadh. Even after Nandas, this practice remained relatively obscure until Islamic sultanates. Thereafter, this became a common practice.
The system of polity seems to be governed by "DharmaShastras" and "Arthashastras" which are ubiquitous all over India, including in the non-aryan clans like Asuras and Nagas. The people talk to each other about "dharma" as if there was some common code of conduct and polity which was accepted by all the sovereigns of India. What that common code was, is not specified, and is not personally known to me. The so called "conquests" or "Dikvijayas" undertaken by various politicians of contemporary India was either for "recognition" and/or ally hunt and/or money and not usually for land. The defeated king swore allegiance to the victorious king and promised to arrive with his resources in the victor's hour of need.