Gravitational wave (GW) detectors, such as LIGO, Virgo, and KAGRA, detect faint signals from distant astrophysical events. However, their high sensitivity also makes them susceptible to background noise, which can obscure these signals. This noise often includes transient artifacts called 'glitches', that can mimic genuine astrophysical signals or mask their true characteristics. In this study, we present DeepExtractor, a deep learning framework that is designed to reconstruct signals and glitches with power exceeding interferometer noise, regardless of their source. We design DeepExtractor to model the inherent noise distribution of GW detectors, following conventional assumptions that the noise is Gaussian and stationary over short time scales. It operates by predicting and subtracting the noise component of the data, retaining only the clean reconstruction of signal or glitch. We focus on applications related to glitches and validate DeepExtractor's effectiveness through three experiments: (1) reconstructing simulated glitches injected into simulated detector noise, (2) comparing its performance with the state-of-the-art BayesWave algorithm, and (3) analyzing real data from the Gravity Spy dataset to demonstrate effective glitch subtraction from LIGO strain data. We further demonstrate its potential by reconstructing three real GW events from LIGO's third observing run, without being trained on GW waveforms. Our proposed model achieves a median mismatch of only 0.9% for simulated glitches, outperforming several deep learning baselines. Additionally, DeepExtractor surpasses BayesWave in glitch recovery, offering a dramatic computational speedup by reconstructing one glitch sample in approximately 0.1 seconds on a CPU, compared to BayesWave's processing time of approximately one hour per glitch.