To simplify the expression \(3\frac{1}{2}-(2\frac{1}{3} \times 1 \frac{1}{4})+\frac{3}{5}\), we can first convert the mixed numbers to improper fractions. \(3\frac{1}{2}\) is equal to \(\frac{7}{2}\). \(2\frac{1}{3}\) is equal to \(\frac{7}{3}\). \(1\frac{1}{4}\) is equal to \(\frac{5}{4}\). So, the expression becomes \(\frac{7}{2}-(\frac{7}{3} \times \frac{5}{4})+\frac{3}{5}\).

Next, we can perform the multiplication inside the parentheses: \(\frac{7}{2}-(\frac{35}{12})+\frac{3}{5}\).

Now, we can find a common denominator for all the fractions so that we can perform the subtraction and addition. The least common multiple of 2, 12, and 5 is 60. So, we can rewrite the expression as \(\frac{210}{60}-(\frac{175}{60})+\frac{36}{60}\).

Finally, we can perform the subtraction and addition: \(\frac{210}{60}-(\frac{175}{60})+\frac{36}{60} = \frac{71}{60}\).

So, the simplified form of the expression is \(\frac{71}{60}\), which can also be written as \(1\frac{11}{60}\). Therefore, the correct answer is C. \(1\frac{11}{60}\).