His plan was explained in that Wiki article...
The Mellon plan
Mellon came into office with a goal of reducing the huge federal debt from World War I. To do this, he needed to increase the federal revenue and cut spending. He believed that if the tax rates were too high, then the people would try to avoid paying them. He observed that as tax rates had increased during the first part of the 20th century, investors moved to avoid the highest rates—by choosing tax-free municipal bonds, for instance.
As Mellon wrote in 1924:
The history of taxation shows that taxes which are inherently excessive are not paid. The high rates inevitably put pressure upon the taxpayer to withdraw his capital from productive business.
If the rates were set more reasonably, taxpayers would have less incentive to avoid paying. His controversial theory was that by lowering the tax rates across the board, he could increase the overall tax revenue.
Andrew Mellon's plan had four main points:
Cut the top income tax rate from 73 to 24 percent
Cut taxes on low incomes from 4 to 1/2 percent
Reduce the Federal Estate tax
Efficiency in government
Mellon believed that the income tax should remain progressive, but with lower rates than those enacted during World War I. He thought that the top income earners would only willingly pay their taxes if rates were 25% or lower. Mellon proposed tax rate cuts, which Congress enacted in the Revenue Acts of 1921, 1924, and 1926. The top marginal tax rate was cut from 73% to 58% in 1922, 50% in 1923, 46% in 1924, 25% in 1925, and 24% in 1929. Rates in lower brackets were also cut substantially, relieving burdens on the middle-class, working-class, and poor households.
By 1926 65% of the income tax revenue came from incomes $300,000 and higher, when five years prior, less than 20% did. During this same period, the overall tax burden on those that earned less than $10,000 dropped from $155 million to $32.5 million.
Mellon also championed preferential treatment for "earned" income relative to "unearned" income. As he argued in his 1924 book, Taxation: The People's Business
The fairness of taxing more lightly income from wages, salaries or from investments is beyond question. In the first case, the income is uncertain and limited in duration; sickness or death destroys it and old age diminishes it; in the other, the source of income continues; the income may be disposed of during a man’s life and it descends to his heirs. Surely we can afford to make a distinction between the people whose only capital is their mettle and physical energy and the people whose income is derived from investments. Such a distinction would mean much to millions of American workers and would be an added inspiration to the man who must provide a competence during his few productive years to care for himself and his family when his earnings capacity is at an end.
Mellon's policy reduced the public debt (largely inherited from World War I obligations) from almost $26 billion in 1921 to about $16 billion in 1930, but then the Depression caused it to rise again. By 1935, Franklin Roosevelt had gone back to high tax rates and wiped out Andrew Mellon's initiatives. The top tax rate went to 80% by 1935 and the federal government increased excise taxes in an attempt to make up for the lost revenue.