Asian markets were mixed on Tuesday as they struggled for direction amid a lack of economic cues.

Australia's S&P/ASX index was trading 0.21% lower or 9.80 points to 5,101.50. The country's central bank cut its policy interest rate on Tuesday.

The Japanese Nikkei was trading 0.60% higher or 86.20 points to 14,344.24. A stronger yen capped gains.

The Shanghai Composite index was trading 0.07% higher or 1.48 points to to 2,051.96

Hong Kong's Hang Seng was trading 1.28% lower or 283.51 points to 21,938.50. The index was pulled down by index heavyweight HSBC.

South Korea's Kospi was trading 0.54% lower or 10.37 points to 1,905.85 points.

The Reserve Bank of Australia (RBA) has cut its cash rate by a quarter percentage point Tuesday, to an all-time low of 2.5%, in line with market consensus. The central bank also hinted at a further cut in rates if needed.

In a statement accompanying the decision, RBA Governor Glenn Stevens cited the local currency as a factor, saying the Australian dollar "has depreciated by around 15% since early April, although it remains at a high level" and that a further easing "would help to foster a rebalancing of growth in the economy."

"The inflation outlook could provide some scope to ease policy further, should that be required to support demand," he added.

Australia is struggling to move away from mining-led growth, prompting the RBA to cut its cash rate. In May, two influential analysts said that Australia needs to slash interest rates in order to plug an economic black hole that was created from slowing mining activity.

'Lower interest rates will likely be required to support domestic demand as Australia transitions away from mining-assisted growth,' Pimco economists Adam Bowe and Robert Mead said in a report published on the company's website.

Wall Street Mixed

On Wall Street, the Dow and the S&P 500 ended lower on Monday. The Nasdaq finished at a 13-year high.

The Dow finished 46.23 points lower at 15,612.13, pulled down by Travelers and United Technologies. The S&P 500 closed 2.53 points lower at 1,707.14.

The Nasdaq ended 3.36 points higher at 3,692.95.

Company Stock Movements

In Sydney, banking stocks were down following the RBA rate cut. Commonwealth Bank of Australia and Westpac shed 0.7% each.

Hearing implant maker Cochlear shot up 2.6%. The company on Tuesday reported a net profit of $132.6m for the 2012/13 financial year, up from $56.8m in the previous year.

Engineering firm Downer shed 0.5% after it reported a 10.3% increase in underlying net profit after tax for the 2013 financial year.

In Shanghai, property stocks were down after the a China Securities Journal report said that the Chinese government must continue with policies to curb the real estate market.

Shares of China Merchants Property, Gemdale and Vanke were all down over 2% each.

Ship builders were down after Beijing asked local governments to halt approvals of new projects, as it attempts to restructure the industry over the next three years.

Guangzhou Shipyard and China State Shipbuilding and fell over 2 percent each.

Dairy producers gave up the previous day's gains after New-Zealand based Fonterra Cooperative Group's CEO apologized for a contaminated milk scare on Tuesday

Xinjiang Western Husbandry fell 5.5% while Royal Dairy shed over 3% after rallying 10% and 7% respectively on Monday

In Hong Kong, HSBC dropped 4.5%, pulled down by concerns that the bank's revenues were being affected by slowing growth in emerging markets.

Revenue fell 7% to $34.4bn as the bank said western economic growth remained muted and growth from emerging market beacons of growth, China and Asia, slowed significantly. However, HSBC aims to streamline the bank's operations, by focusing on high-growth markets in Asia, despite the economic slowdown.

In Tokyo, consumer electronics major Sony dropped 5% after it rejected investor Daniel Loeb's proposal to spin-off its entertainment unit

Mitsubishi Materials gained 2.6% on news that its group operating profit for the first quarter is expected to have risen more than 30% on year to about ¥15 billion ($153m)

Electronics major Toshiba shot up 1.4% on news that it plans to build a NAND flash-memory factory with SanDisk. The two companies will invest about ¥400bn (about $4bn) in the unit that will be built in Japan

Tokyo Electric Power (Tepco) jumped 1.4% even after Japan's nuclear watchdog announced that highly radioactive water from its crippled Fukushima Daiichi nuclear plant has seeped into the ocean. Tepco confessed last month that radioactive groundwater from the power plant has leaked into the sea.

Truck maker Isuzu Motors inched up 0.3% on news that the company is expected to pose record operating profits.

In Taiwan, phone maker HTC fell 3.2% after it reported posted a 37% year-on-year drop in revenue in July.

In Seoul, index heavyweight Samsung Electronics fell 1%, following an earlier 2% drop. Samsung's lost more than $1bn in market value on Monday after the US government revoked a ban on the sale of some Apple devices in the US, reversing a June ruling that favoured the South Korean smartphone maker.

Shares of LG Electronics and LG Display gained 3% each on a stronger Japanese yen.