In this paper, we propose a scalable approximate multiplier design, scaleTRIM, that approximates the multiplication operation using fitted linear functions, also referred to as linearization. We show that multiplication operations can be completely replaced by low-cost addition and bit-wise shift operations by exploiting linearization. Moreover, our proposed design utilizes a lookup table (LUT)-based compensation unit as a novel error-reduction method. In essence, input operands are truncated to a reduced bit-width representation (i.e., h bits) based on their leading-one positions. Then, a curve-fitting method is employed to map the product term to a linear function. Additionally, a piecewise constant error-correction term is used to reduce the approximation error. To compute the piecewise constant, we divide the function space into M segments and average the errors within each segment. In particular, our multiplier supports various degrees of truncation and error compensation to offer a range of accuracy-efficiency trade-offs. The proposed multiplier improves the Mean Relative Error Distance (MRED) by about 15.2% while satisfying the efficiency constraint and improves the Power Delay Product (PDP) by about 22.8% while satisfying the accuracy and efficiency constraints compared to different state-of-the-art approximate multipliers. From a usability perspective, our evaluation of the proposed design for image classification using Deep Neural Networks (DNNs) demonstrates that scaleTRIM offers a better accuracy-efficiency trade-off than state-of-the-art approximate multiplier designs.