Does the body have a mechanism for cleaning plaque buildup in arteries?
Atherosclerosis can be reversed to some extent by certain diets and change in life style that result in decrease of excessive weight, blood pressure and cholesterol levels.

Studies

1) Dietary Intervention to Reverse Carotid Atherosclerosis (Circulation, 2010)

In a study in Israel, in 140 participants, who were mostly age 40-65 and overweight, they observed an average of 5% reduction of the the volume of the carotid artery wall, which reflects the reduction of the plaque.


  Two-year weight loss diets can induce a significant regression of
  measurable carotid VWV [vessel wall volume]. The effect is similar
  in low-fat, Mediterranean, or low-carbohydrate strategies and appears
  to be mediated mainly by the weight loss–induced decline in blood
  pressure.


2) Intensive Lifestyle Changes for Reversal of Coronary Heart Disease (JAMA, 1998)

Forty-eight patients with moderate to severe coronary heart disease were randomized to an intensive lifestyle change group (10% fat whole foods vegetarian diet, aerobic exercise, stress management training, smoking cessation, group psychosocial support) or to a usual-care control group, and 35 completed the 5-year follow-up quantitative coronary arteriography.


  Experimental group patients (20 [71%] of 28 patients completed 5-year
  follow-up) made and maintained comprehensive lifestyle changes for 5
  years, whereas control group patients (15 [75%] of 20 patients
  completed 5-year follow-up) made more moderate changes. In the
  experimental group, the average percent diameter stenosis at
  baseline decreased 1.75 absolute percentage points after 1 year (a
  4.5% relative improvement) and by 3.1 absolute percentage points after 5 years (a 7.9% relative improvement). In contrast, the
  average percent diameter stenosis in the control group increased by
  2.3 percentage points after 1 year (a 5.4% relative worsening) and by 11.8 percentage points after 5 years (a 27.7% relative worsening) (P=.001 between groups. Twenty-five cardiac events occurred in 28
  experimental group patients vs 45 events in 20 control group patients
  during the 5-year follow-up (risk ratio for any event for the control
  group, 2.47 [95% confidence interval, 1.48-4.20]).
  
  The experimental group reduced LDL cholesterol levels by 40% at 1 year
  and by 20% after 5 years.
  
  When we began this study, we believed that the younger patients with
  milder disease would be more likely to show regression, but we did not
  find this to be true. Instead, we found that the primary determinant
  of change in percent diameter stenosis in the experimental group was
  neither age nor disease severity but adherence to the recommended
  changes in diet and lifestyle.
  
  those who gained weight were more likely to show progression of atherosclerosis. 
  
  Experimental group patients had a 91% reduction in reported frequency
  of angina after 1 year and a 72% reduction after 5 years (Table 5). In
  contrast, control group patients had a 186% increase in reported
  frequency of angina after 1 year and a 36% decrease in frequency after
  5 years.


Mechanisms

Reversal of atherosclerotic plaques can be achieved by removing the causes. According to Atherosclerosis: Process, Indicators, Risk Factors and New Hopes, (Int J Prev Med, 2014), decreasing excessive body weight + exercise + cholesterol-lowering diet + cessation of smoking can result in:


Less damage to the arterial intima
Higher HDL/LDL ratio, meaning adequate removal of LDL (by HDL) from the blood into the liver and thus less deposition of cholesterol into the arteries
Less inflammation in the arterial intima