The question isn't so much 'Why did GDP plummet in 1975?' as 'Why did it grow so rapidly from 1973-1975?'

Bangladesh won its independence from Pakistan in 1971. It did so, however, as an impoverished nation. The war had begun with the Pakistani Army siezing control of the major population centres, destroying infrastructure, and harrying the surrounding countryside. Up to 3 million Bangladeshis died during the war, with the educated classes being particularly targeted. Capital fled from the country, as many of the commercial enterprises were owned by West Pakistanis.

Despite this, the economy of Bangladesh did not collapse straight away. International aid was forthcoming from India, who had supported the country during the war, and had positive ties with the ruling Awami Leauge. Economic links were also formed with Soviet Bloc countries, including aid being sent, though assistance from the West was less forthcoming. Whether this was a result of reluctence of Western nations to assist a socialist governing party or a result of the Leauge's own reluctance to deal with the West is still a debated issue.

That changed in 1973. The global oil crisis increased the need for aid dramatically, whilst also inhibiting the amount availible from Soviet and Indian sources. This led to renewed efforts to secure support from the West. This succeeded, but was conditional on the removal of the left wing finance minister, the privatisation of publicly owned resources, and the devaluation of the currency.

GDP rose steadily as a result of the influx of new aid and market resources. But the cost was high. These measures exarcebated the already sharp inequality between urban commercial and agrarian rural areas. Widespread famine resulted the following year. The cause of the severity of this is also debated: a shortage in production, inefficient distribution, and the refusal of the US to allow food aid while the country maintained trade links with Cuba have all been blamed.

That led to a precarious political situation. Awami Leauge members were often the targets of violence. President Mujib declared a state of emergency at the end of 1974, formed a new political party (BAKSAL), banned opposition parties, and restricted rights to protest and assemble.

The army intervened on the 15 August 1975, assasinating Mujib and all of his family present in the country. The military government, although it was to last until 1990, at first appeared out of control. Coup led to counter-coup led to counter-coup, with several generals sieing and being removed from power in quick succession. Needless to say, aid dried up, investment proved near-impossible to attract, and the rebuilding effort slowed down in the face of an uncertain future.

So, though GDP did drop in 1975 as a result of the unrest, uncertainty and the military intervention, in some ways it was a simple reversion to the pattern you see in evidence before 1973. It's those 2 years of extreme GDP-growth that are the exception, and which were untenable to maintain in the long run.

Refs: D. Lewis (2011) Bangladesh: Politics, Economy and Civil Society. L. Ziring (1992) Bangladesh from Mujib to Ershad