The left-winger's comments came as Chancellor Rachel Reeves doubled down on plans to reform benefits.
Campaigners have hit out at plans to save £5billion by tightening eligibility for Personal Independence Payment and changing the system for incapacity benefits.
Figures are expected this week on the effect the reforms will have on poverty levels.
Speaking to Holyrood Magazine, Leishman said: "There is absolutely no doubt in my mind that these cuts are going to impoverish already vulnerable, disadvantaged people living in our society today.
"These are the people that we should be throwing our arms around and helping" The Alloa and Grangemouth MP added: "It's a measurement of any society how the government treats those who are in need and, by cutting that much from the welfare budget, there is no doubt in my mind that we cannot claim there is no austerity under Labour if we are going to cut that much money from welfare." Reeves will this week announce an update on the economy through her Spring Stateme...