To find the coefficient of \(x^3\) in the expansion of \(\left( 2 - \frac{1}{2}x \right)^7\), we use the binomial theorem:

\(\binom{n}{k} a^{n-k} b^k\)

where \(n = 7\), \(a = 2\), \(b = -\frac{1}{2}x\), and we need the term where the power of \(x\) is 3.

Thus, \(k = 3\) and the term is:

\(\binom{7}{3} (2)^{7-3} \left(-\frac{1}{2}x\right)^3\)

Calculate each part:

\(\binom{7}{3} = 35\)

\((2)^4 = 16\)

\(\left(-\frac{1}{2}\right)^3 = -\frac{1}{8}\)

Combine these to find the coefficient:

\(35 \times 16 \times -\frac{1}{8} = -70\)

Therefore, the coefficient of \(x^3\) is \(-70\).