There are two kinds of graduation marks on a stick, using the principle of inclusion and exclusion.

Because the least common multiple of 10 and 12 is 60,

Then let's assume that the length of this stick is 60 cm, 60÷ 10=6 (cm), and 60÷ 12=5 (cm).

10 is the first scale line, totaling 10- 1=9 (bar).

12 is the second graduation line, totaling12-1=11(bar).

The number of lines overlapping with the first tick mark and the second tick mark: the least common multiple of 6 and 5 is 30,60 ÷ 30-1= 2-1=1(lines).

Therefore, there are 9+11-1=19 in total.

The stick was sawed into 19+ 1=20 (segments);

The stick was sawed into 20 pieces.

So the answer is: 20.