In South Korea, the Kospi added 0.17 percent or 3.55 points to close up 2,041.94, while Hong Kong's Hang Seng slipped 0.48 percent by 3:00 pm local time.
The Hong Kong benchmark has fallen about 5 percent in the past two weeks.
"The selling was accompanied by emerging market outflow as the U.S. dollar surged to a decade's high. The fast depreciation of yuan has also urged outflow from the China market, further weighing on Hong Kong equities," explained Margaret Yang, market analyst at CMC Markets, in a note on Tuesday.
The Shanghai composite ended down 0.5 percent or 15.61 points at 3,102.48, and the Shenzhen composite closed 0.14 percent or 2.78 points lower at 1,981.32.
The Chinese yuan midpoint was set at 6.9468 on Tuesday versus its last close at 6.9513. The yuan last traded at 6.9506 against the dollar and at a eight-year low.
Investors worry that the capital outflows seen post-Trump's victory and a weakening yuan could derail an economy that has shown recent signs of stabilization, Reuters reported.
Overnight, major U.S. indexes closed higher in low volume trade. The Dow Jones industrial average closed up 0.2 percent at 19,883.06 and the S&P 500 gained 0.2 percent to 2,262.53, while the Nasdaq composite finished up 0.37 percent at 5,457.44.
In currency markets, the dollar regained some momentum, with the dollar index, which measures the greenback against a basket of currencies, up at 103.41, compared with levels around 102 yesterday.
The stronger greenback weighed on Asian currencies, with Malaysia's particularly hard-hit.
The dollar was fetching 4.4775 ringgit as of 3:02 pm HK/SIN, with the Malaysian currency touching its lowest since January 1998, during the Asian Financial Crisis. The emerging market currency has been whacked by the surging dollar after President-elect Donald Trump's surprise win, tumbling 11 percent since Nov. 8.