The British lender, which survived the 2008 crisis without state aid unlike many of its rivals, announced in a strategic review that it would seek to save $2.5-3.5 billion (1.7-2.4 billion euros) in costs by 2013.
"Headcount clearly will be lower," chief executive Gulliver told reporters in London, the headquarters of Europe's biggest bank.
Shares in HSBC fell 1.54 per cent to close at 646.1 pence on London's FTSE 100 index, which dropped 0.71 per cent to 5,976 points.
"The new chief executive is clearly attempting to stamp his mark on the company," said Keith Bowman, an analyst at Hargreaves Lansdown Stockbrokers.
Gulliver, who took the reins in January and unveiled mixed first-quarter earnings on Monday, said the enormous cost savings would be ploughed back into fast-growing markets around the world, notably Asia.
"Our strategy is to be the leading international bank, concentrating on commercial and wholesale banking in globally connected markets," Gulliver said in the bank's strategy update.
HSBC will also conduct a separate assessment of its US branch network and cards business, which Gulliver said could be sold -- but only for a "sensible" price. Other cash-saving measures include a streamlining of IT operations.
"What we have seen recently is a large group of companies that have newly appointed chief executives undertaking a change of strategy -- of which HSBC is an example," said Atif Latif, director of trading at Guardian Stockbrokers.
Gulliver "has to make some bold calls to make sure that growth areas are maintained and operations where there seems to be limited upside are being wound down.
"The focus for cost efficiency -- by closing down underperforming units and dealing with for example the US arm -- shows that tough calls are being made to streamline operations," added Latif.
HSBC chairman Douglas Flint told journalists that it was the first time in four years that the bank had choices, having dealt with the fallout from the global financial crisis.
"Today we can look forward, and look forward with confidence," he told reporters.
HSBC had on Monday announced that the bank's net profits surged 58 per cent to $4.15 billion in the first quarter on lower taxes and bad debts.
However, it also revealed that its pre-tax gains were pushed down by rising staff costs and by money set aside to compensate customers in Britain who were mis-sold credit insurance.
Gulliver on Wednesday said that high inflation across Asia was pushing up wages in China and India, although this was being offset by strong growth in these countries.
Gulliver, HSBC's former head of investment banking whose hiring was announced last September, replaced Michael Geoghegan who stepped down after he reportedly lost a boardroom battle for the chairman's job.
There have meanwhile been persistent reports in the British media that the lender is looking at the possibility of switching its headquarters to Hong Kong from London to reduce the group's tax burden.
HSBC was founded in Hong Kong and Shanghai in 1865 and the bank regards Asia as its most important region.